Yudhoyono described Boediono as a devout Muslim who would help him bring a "clean and responsible government".
Anton Gunawan, chief economist at Danamon Bank, said Boediono was "probably the cleanest out there".
"Even when he was a minister he still lived in his own house and doesn't like to have the official car. He catches the train," he said.
Boediono said he was "ready to start working from today".
The Reuters news agency reported sources in the central bank as saying that Boediono had submitted his resignation on Friday, news that prompted a stock market sell-off on concerns about the course of monetary policy.
While the president is heavily tipped to be re-elected in the July polls, if the vote goes in to a second round, the election may not be decided until October.
That has raised uncertainty in financial markets over when a replacement for Boediono might be found at the bank.
As well as announcing his running mate, Yuhhoyono said that his Democrat party would team up with a group of smaller parties, including the Islamic Prosperous Justice Party (PKS), to form a coalition in the next parliament.
Although the Democrats won one-fifth of the votes in last month's parliamentary election, giving the party the biggest share of seats, Yudhoyono has wooed other parties to ensure the government would have enough support in parliament.