Mr Bush with son George W Bush at St Martin’s Episcopal Church for a funeral service for former first lady Barbara Bush (AP Photo/David J. Phillip, File)
In a statement, he added: "The entire Bush family is deeply grateful for 41's life and love, for the compassion of those who have cared and prayed for Dad, and for the condolences of our friends and fellow citizens."
The former president served from 1989 to 1993, and eight years later watched his son George W became the 43rd president - only the second father-and-son chief executives, following John Adams and John Quincy Adams.
The elder Mr Bush, the son of a senator, rose through the political ranks: from congressman to UN ambassador, Republican Party chairman to envoy to China, CIA director to two-term vice president under the hugely popular Ronald Reagan.
He entered the White House in 1989 with a reputation as a man of indecision and indeterminate views.
Statement from President Donald J. Trump and First Lady Melania Trump on the Passing of Former President George H.W. Bush pic.twitter.com/qxPsp4Ggs7
America has lost a patriot and humble servant in George Herbert Walker Bush. While our hearts are heavy today, they are also filled with gratitude. Our thoughts are with the entire Bush family tonight – and all who were inspired by George and Barbara’s example. pic.twitter.com/g9OUPu2pjY
George HW Bush talks with a group of young people at a rally in Houston, Texas, in 1970 (AP Photo/File)
After winning United Nations support and a green light from a reluctant Congress, he unleashed a punishing air war against Iraq and a five-day ground juggernaut that sent Iraqi forces reeling in disarray back to Baghdad.
He basked in the biggest outpouring of patriotism and pride in America's military since World War II, and his approval ratings soared to nearly 90%.
George HW Bush with Margaret Thatcher (Tim Ockenden/PA)
His legacy was dogged for years by doubts about the decision not to remove Saddam Hussein. The Iraqi leader was eventually ousted in 2003, in the war led by Mr Bush's son that was followed by a long, bloody insurgency.
The elder Mr Bush's prime interest was foreign policy. Under his watch, the Berlin Wall came down, the Warsaw Pact disintegrated and the Soviet satellites fell out of orbit.
The other battles he fought as president, including a war on drugs and a crusade to make American children the best educated in the world, were not so decisively won.
He rode into office pledging to make the United States a "kinder, gentler" nation and calling on Americans to volunteer for good causes, to create "a thousand points of light".
Mr Bush lost his bid for re-election to Bill Clinton in a campaign in which businessman H Ross Perot took almost 19% of the vote as an independent candidate.
Paying tribute to Mr Bush, current US president Donald Trump praised his "sound judgment, common sense and unflappable leadership".
In a joint statement with wife Melania, he added: "Through his essential authenticity, disarming wit, and unwavering commitment to faith, family and country, President Bush inspired generations of his fellow Americans to public service - to be, in his words, "a thousand points of light" illuminating the greatness, hope and opportunity of America to the world.
"President Bush always found a way to set the bar higher."
He said: "Along with his full life of service to country, we will remember President Bush for his devotion to family - especially the love of his life, Barbara.
"His example lives on, and will continue to stir future Americans to pursue a greater cause."
Barack Obama, the 44th president of the US, said America had "lost a patriot and humble servant".
He said: "While our hearts are heavy today, they are also filled with gratitude.
"George HW Bush's life is a testament to the notion that public service is a noble, joyous calling. And he did tremendous good along the journey... It's a legacy of service that may never be matched, even though he'd want all of us to try."
Meanwhile, Taoiseach Leo Varadkar extended his sympathies to the Bush family.
He said George HW Bush was "a notable President who left his mark on US politics".
President Michael D Higgins said: "People in Ireland will have learned with sadness of the death of former President of the United States of America, George H.W. Bush.
He said Mr Bush will be remembered "for his long life of public service to the people of the United States and as a President who led his country at a period of significant change at national and global level."
Mr Higgins noted that the 1980s to the mid-1990s was a period of deep challenges to the multilateral institutions.
He also said; "To his Presidency of the United States he brought all of the energy and the values he cherished, drawn from his Texas and Massachusetts roots."
Mr Higgins said he will also be remembered "for the directness with which he expressed his policy principles and his efforts to achieve bipartisanship".
He added: "On behalf of the Irish people I offer our deepest sympathies to his family and to the people of the United States."
And, in the UK, John Major has paid tribute to President George HW Bush following his death.
He said: "George HW Bush was above all else a family man and, for him, the American people were part of that family.
"In public office he served as he lived, with compassion, courage, dignity and grace. As president, he saw America's obligation to the world and honoured it - and he remained committed to public service until the day he died.
"I feel privileged to have worked with him, and even more privileged that he became a lifelong friend. He was, quite simply, one of the most deep down decent people I have ever known.
"Our hearts go out to his family, but they will take great comfort in the knowledge that their brother, father, grandfather and great-grandfather is now reunited with his beloved wife Barbara, and their daughter Robin."
UK Foreign Secretary Jeremy Hunt tweeted: "Deeply sorry to hear of death of President George HW Bush. A true friend of the UK and a deeply wise man whose leadership made the world more safe and more free. Sincerest condolences to the Bush family and the American people from your friends in Britain."