He became the 11th Fianna Fail TD to announce that he would not be running in the General Election.
Mr Killeen, who previously battled bowel cancer, said his decision to retire from politics was not because of a health setback, but because he would not have the energy to canvass in the upcoming General Election.
Mr Finneran said he had decided to retire because he had passed his "sell-by date" after 32 years in politics.
The junior minister, who got 10,000 votes in the last general election, denied his decision was motivated by the prospect of Fianna Fail being wiped out in the General Election.
The departure of 75-year-old Mr Woods had been expected given his age and the length of his career in the Dail.
He served as a cabinet minister in five different departments and under five different Taoisigh.
In a statement last night, Mr Woods said he wanted to thank all the people in his Dublin North East constituency who he had served as a TD "through good times and bad" over the past 33 years.
Mr Woods introduced the carer's allowance, set up the Money Advice and Budgeting Service (MABS), the social welfare Christmas bonus (now abolished), approved the building of Beaumont Hospital in Dublin and increased the number of special-needs assistants in classrooms.
However, as Education Minister he was also responsible for signing the controversial deal with the religious orders which capped their liability for sexual abuse cases at €128m. It proved to be totally inadequate to cover the eventual compensation cost of €1.3bn, and the religious orders agreed to pay a further €348m in 2009.
Taoiseach Brian Cowen paid tribute to Mr Woods last night for serving the country with great intelligence, insight, and true dedication.
"His many achievements as a minister are characterised by a desire to help the less well-off in our society and to do his utmost to improve the standard of living for everyone in our country," he said.
Meanwhile, it emerged yesterday that Mr Cowen put no pressure on departing ministers Mr Killeen and Mr Finneran to stay on and fight the next election.
Both ministers said yesterday that Mr Cowen had accepted their decisions not to run again.
Mr Killeen said not contesting the election was the only "responsible course of action" for him and his family.
Some of his political work during his bowel cancer treatment had not been the sensible thing to do or what the doctors advised, he said.
"I am probably suffering for that in terms of some of the difficulties that I have and people close to me will be aware that there are some ongoing difficulties that I am not as well able to surmount as I was," he said.
- Fianna Fail last night selected Councillor Declan Breathnach and Senator James Carroll as their Louth candidates for the General Election.
Senator Carroll was the only candidate for Louth south at last night's selection convention in Drogheda. Cllr Breathnach was selected for Louth north ahead of his councillor colleagues Sean Bellew and Liam Reilly.