"I'm here to say goodbye to a good friend," Bush said in a ceremony in the Roosevelt Room. "There's no finer man in public service than Rob Portman."
"Fortunately we've found a good man to succeed him," Bush said of Nussle. "Jim's name and knowledge command respect on Capitol Hill."
Nussle ran for governor of Iowa last year and was defeated. He has been serving in Iowa as an adviser in former New York Mayor Rudy Giuliani's campaign for the Republican presidential nomination.
Portman said he was leaving the administration for personal reasons. His family has remained in Cincinnati and he has been commuting home on weekends for 14 years.
"I need to be home more. I've got three kids ages 12 to 17. It's just been very hard to spend as much time with them and Jane as I need to at this time of my life," he said.
Portman also made it clear he might seek a return to elective office, either by running for governor of Ohio or for the Senate.
Portman said the president "is in a good position" to contest the Democratic-controlled Congress over spending if necessary. The White House has issued some veto threats against spending bills in recent days, and more are coming, the budget director said.
Nussle's appointment is subject to Senate confirmation.
He was first elected to Congress in 1990, and quickly distinguished himself as a member of the "Gang of Seven," a group of young Republicans who demanded changes in the methods the Democrats used to run the House.
He later served three terms as chairman of the House Budget Committee, where he favored budget plans that accommodated Bush's tax cuts as well as the spending restraint that conservative Republicans advocated.
Portman entered politics as a New Hampshire advance man on the 1980 presidential campaign of George H.W. Bush. He worked as a White House lobbyist in the first President Bush's administration and later played the role of Sen. Joe Lieberman, D-Conn., in Dick Cheney's vice presidential debate preparations in 2000. Four years later, Portman again impersonated the Democratic vice presidential candidate, Sen. John Edwards, D-N.C., in Cheney's debate preparations.
In Congress, Portman was a top liaison between Congress and the Bush White House, working behind the scenes from his posts on the Budget Committee and the powerful tax-writing Ways and Means Committee.
As trade representative, he was key to finessing House passage of the Central American Free Trade Agreement but had less success in pushing forward global trade negotiations.