In a statement, Blair said: "Jack's contribution to law and order in Britain and this country's standing in the world is quite simply formidable.
"In 2015, Parliament will lose one of the most able politicians of my generation, but I have no doubt that he will be immensely successful in whatever he turns his hand to next."
More top news
Theresa May could face a Tory rebellion as MPs demand to see her plan for Brexit.
"I've never told anyone that before," she told the Today Show on a visit to a homeless shelter in New York.
Find out where the year's political shocks and England's football failure rank, plus the UK's most followed celeb and most talked about TV.