Free-wheeling presidential trouble-shooter Joseph W. Canzeri resigned yesterday to spare the Reagan administration embarrassment over favorable home loans and two incidents of double billing for expenses.

A White House spokesman acknowledged that Canzeri's acceptance of below-market terms for financing a $380,000 Georgetown townhouse was being evaluated by the Justice Department, which is also looking into Canzeri's double billing of travel expenses to the White House and the Republican National Committee.

"No one in the administration has advised me or encouraged me to step aside but I do believe that this action is in the best interests of you and the administration," Canzeri said in a letter to President Reagan which he composed late yesterday afternoon in the office of White House deputy press secretary Larry Speakes.

As executive assistant to White House deputy chief of staff Michael K. Deaver, Canzeri was noted as a no-nonsense scheduling official in charge of advance arrangements, who smoothed out bumpy logistics first in the Reagan presidential campaign and then in the White House.

But Canzeri ran into difficulty last week when the double billings on two advance trips were discovered by White House Counsel Fred F. Fielding. Canzeri said the double billings were "an honest mistake."

Canzeri, who worked for the Rockefeller family for 17 years, said he also had done nothing improper in accepting a 9 per cent loan from Laurance S. Rockefeller and California developer Donald M. Koll to buy a $380,000 townhouse in Georgetown.

"If you asked anyone in the world where I'd go for a loan, there would never be any doubt," he said.

Known as a high-style advance man during Nelson A. Rockefeller's presidential campaigns, Canzeri was brought into the Reagan campaign in 1980 by Deaver, a close Reagan aide who had developed an appreciation of Canzeri's abilities in the days when Reagan and Rockefeller were political rivals and governors of the nation's two most populous states.

Deaver yesterday said he was sorry but not surprised to see Canzeri's quick resignation.

"His first reaction was: 'I don't want to hurt the president,' " Deaver said. "Everybody's going to miss him. It didn't surprise me that he did this of his own volition. That's the kind of guy he's been from the beginining. He always brought the added little touch. He gave us just a little bit more class."

According to White House officials, Fielding was making a routine examination of expense billings when he found that Canzeri had charged expenses from two trips both to the White House and the Republican National Committee.

One of the trips involved a group dinner in San Diego on March 29, 1981, where Canzeri was advancing President Reagan's scheduled trip to Mexico. Reagan was wounded in an assassination attempt the next day and did not make the trip. The other double billing was for a similar dinner last June in Paris, where Canzeri was advancing a trip for Bush.

When Fielding called the incidents to Canzeri's attention, he said they were "an oversight" and wrote out a check to the Republican National Committee.

Last Thursday, Canzeri was called by a New York Times reporter who inquired about the terms of the loan Canzeri received from Rockefeller and Koll after his attempt to arrange a conventional mortgage loan ran into trouble. Canzeri said yesterday he decided on the spot that he should resign, even though he saw "nothing wrong" in securing the loan and would do it again.

"I've been around this business for a long time and I don't want to embarrass the president," Canzeri said yesterday in an emotional moment. "In my job if you have to stop and think before you do everything, you're no good."

In his days as a Rockefeller advance man, Canzeri was known for providing lavish meals and plush accommodations for politicians and traveling press. He has a ready wit and a quick temper, and he occasionally chafed at the strict accounting practices that present laws require of political candidates.

"Nelson never thought small," Canzeri said earlier this year in recounting his years with Rockefeller. "There was no such word as 'no.' "

Canzeri brought his free-wheeling style and command of logistical detail to the Reagan campaign in 1980 when that campaign was in need of both qualities. Reagan liked Canzeri but couldn't remember his name and called him "Canzoni" for several weeks.

It stuck as a nickname, and others began calling him "Canzoni" as well. When Reagan heard about this, he became embarrassed and told Canzeri he could call him "Regan."

In the White House, Canzeri was an advocate of presidential openness on trips and sometimes clashed with security officials who wanted to keep Reagan heavily protected. For several months stories have circulated around the White House that Canzeri would soon leave because of accumulated frustrations.

Yesterday, he bowed out with emotion, calling his work for Reagan "the highlight of my life."

But he recovered his sense of humor soon afterward, quipping to a reporter who asked him what he would do next: "I don't know. I'll either become a mortgage banker or a certified public accountant."