A delighted Heaslip, helped by a stellar performance against Biarritz on Saturday, tweeted: "Dreams do come true..."
Ireland captain Jamie Heaslip had been among those who it was thought was under pressure for a place but he now looks destined to contest the Test number eight jersey with Wales' Toby Faletau.
Wales star Sam Warburton has been named British and Irish Lions captain for this summer's tour of Hong Kong and Australia with Brian O'Driscoll and Paul O'Connell overlooked for the post.
There are no places among the 38-man squad announced by Lions manager Andy Irvine in London today for England skipper Chris Robshaw or 2003 World Cup hero Jonny Wilkinson, who turned down a place in the squad, Warren Gatland revealed.
But head coach Warren Gatland handed surprise call-ups to Scotland wing Sean Maitland, England prop Mako Vunipola and 2005 Lions tourist Matt Stevens.
Cardiff Blues flanker Warburton, at 24 the youngest Welsh Lions captain in history, will lead a squad comprising 14 of his compatriots.
Warburton led Wales to the 2011 World Cup semi-finals - Wales' best performance for 24 years - and a Six Nations Grand Slam five months later.
After being injured for the opening part of this season's Six Nations, he returned to deliver a man of the match display against Scotland and then starred when Wales inflicted a record 30-3 defeat on England to win the title.
While Wales are celebrating their largest Lions contingent since 16 players travelled to New Zealand 36 years ago, England provide 10 members of Gatland's squad, one more than in South Africa four years ago.
Stevens, who missed the 2009 tour while serving a two-year drugs ban, retired from England duty after the 2011 Rugby World Cup but has been included as one of three tight-head options.
There are nine Irishmen in the travelling squad but there was no place for Ulster hooker Rory Best, with England's Dylan Hartley and Tom Youngs selected along with Wales' Richard Hibbard.
Scotland provide three players - the New Zealand-born wing Maitland, lock Richie Gray and full-back Stuart Hogg.
Warburton admitted he had known about the news for some time, saying: "Warren gave me a call, it's been nine or 10 days since I found out and the biggest secret I've had to keep.
"It's unbelievable, an accolade very few people achieve and it's an unbelievable honour."
Gatland said: "In the last two or three years he's been the most successful captain in the northern hemisphere.
"I have a huge amount of respect for Sam, he's an absolute professional and he leads from the front."
Gatland admitted it had been tough to leave out the likes of Robshaw and Wilkinson.
"There was a robust debate about the squad and there were healthy discussions for every position," he said.
"Some real quality players have missed out. We had a thorough process and it's been tough."
He did offer hope to those left out, however, saying: "If you look at previous tours six to eight players get injured and there will be a group of back-up players who can be called upon."
Much of Gatland's squad was as expected, spearheaded by the likes of Ireland centre Brian O'Driscoll, who is on his fourth successive Lions tour, 2009 captain Paul O'Connell and Wales prop Adam Jones.
But there are also opportunities for a new generation of Lions, players such as Wales trio George North, Alex Cuthbert and Justin Tipuric, England pair Manu Tuilagi and Owen Farrell and Ireland prop Cian Healy.
Gatland's squad is split into 16 backs and 21 forwards and four weeks today the party will leave for Hong Kong where they open the 10-match tour against the Barbarians on June 1.
The Lions then head to Australia with the first of three Tests against the Wallabies in Brisbane on June 22.
Robshaw becomes the third England captain of the professional era to be overlooked by the Lions, following Phil de Glanville in 1997 and Steve Borthwick four years ago.
It is particularly rough justice on the Harlequins flanker who led England to within one win of the Six Nations title and the Grand Slam this season.
Other notable absentees from the England fold include Tom Wood, Chris Ashton, Brad Barritt, Joe Launchbury, Ben Morgan and Danny Care.
Wales, though, will send to Australia 14 of the starting line-up that accounted for England just over six weeks ago.
The exception is Ospreys fly-half Dan Biggar.
Flanker Dan Lydiate has received the nod from Gatland despite being in the early stages of his comeback from a serious ankle injury he suffered playing for Newport Gwent Dragons last September.
Lydiate, the 2012 Six Nations player of the tournament, missed Wales' entire autumn Test series and this year's championship, but Gatland knows full well his capabilities.
Glasgow wing Maitland, 24, has been fast-tracked into the Lions squad after moving from New Zealand this season and making his Scotland debut in the Six Nations.
Maitland qualifies for Scotland through his Glaswegian grand-parents, who emigrated to New Zealand in the 1960s and he has seen off the Ireland wing Simon Zebo, who was strongly fancied to make Gatland's final cut.
Gray and Hogg complete the Scottish contingent but there was no place for their Six Nations captain Kelly Brown in a highly-competitive back row area.
The 37-man British and Irish Lions squad selected by head coach Warren Gatland for the tour of Hong Kong and Australia: L Halfpenny, S Hogg, R Kearney, G North, A Cuthbert, T Bowe, S Maitland, B O'Driscoll, M Tuilagi, J Roberts, J Davies, J Sexton, O Farrell, C Murray, M Phillips, B Youngs, G Jenkins, C Healy, M Vunipola, A Jones, D Cole, M Stevens, D Hartley, R Hibbard, T Youngs, I Evans, R Gray, AW Jones, P O'Connell, G Parling, T Croft, T Faletau, J Heaslip, D Lydiate, S O'Brien, J Tipuric, S Warburton (capt).