Mr Blair is in Iraq to "meet the prime minister (Nouri al-Maliki) and members of the government," a spokesman at Blair's office in London said, adding there would be a press conference later.
Journalists travelling with Mr Blair said he took a helicopter ride into Baghdad's heavily-fortified Green Zone, where the US-led coalition and Iraqi prime minister's office are based, after first flying to Kuwait from Britain.
The British leader's official spokesman said in Baghdad that Mr Blair will seek to shore up the 37-member cabinet which was finally approved by Iraqi MPs on Saturday after more than five months of coalition talks.
"Iraq now has a democratically-elected government which is there for a four-year term, is made up of all the different groupings within Iraq and it is very much dictating the agenda," the spokesman said.
"We are here to show our support for that democratic government and to help it take charge of its own destiny," he added.
A senior British official travelling with Blair said the withdrawal of the US-led multi-national force should be accomplished within four years, with a transfer to civilian control in several provinces during the summer.
He stressed that was not a timetable for troop withdrawal, and did not augur the quick return home of large numbers of British troops.
Around 8,000 British troops remain in Iraq, in and around the main southern city of Basra.