Mayor Marian Barry yesterday appointed Philip M. Dearborn, an expert in financial matters and a past critic of the way Barry has handled the city's budget crisis, to the newly created post of financial counselor of the mayor.

Dearborn will take a six-month leave of absence from him position as vice president of the Greater Washington Research Center to advise the mayor on what fiscal policies to adopt and how to implement them, Barry announced. He will begin his new duties, which will carry no direct administrative authority, on Monday.

In addition to his role as adviser, Dearborn will serve as chief spokesman on financial matters for a District of Columbia government, whose policies he has attacked in the past.

"I guess that's part of the reason why I'm being asked to do this," Dearborn said yesterday of his past criticism of the ways in which Barry has attempted to solve the city's financial crisis. "No longer will I be sitting in an ivory tower making suggestions. I'll have to make sure things get done."

During the early months of the budget crisis last year, Dearborn repeatedly expressed skepticism that the city government had a handle on the problem. He criticized the city's accounting procedures as inadequate, said he doubted that a cost-cutting program established by Barry would work, and complained that the city had a chronic inablity to produce necessary data.

The city will pay Dearborn at the rate of $50,112 a year during his six-month appointment, Barry said.

The appointment of an overall financial coordinator was one of a number of recommendations made last year by Lazard Freres and Co., the New York investment firm hat has been advertising Barry on how to solve the budget crisis and enter the municipal bond market. Barry rejected the recommendation at the time, but over the months "it just became clear this was needed," a spokesman for the mayor said.

Dearborn's appointment follows the release earlier this week of the first-ever full audit of the city's books, which showed that the city rolled up a $105 million deficit during the 1980 fiscal year.

Dearborn's first task, begun even before his appointment was announced, was to aid in the development of a single plan to finance the city's accumulated budget deficit. Barry, City Council Chairman Arrington Dixon and D.C. Del. Walter E. Fauntroy, all of whom suggested proposals of their own, scheduled a joint press conference for this afternoon to announce the common plan.

Dearborn said that his main function will be to make sure that city officials work in coordination with one another. He will have no executive authority, but his advice will flow through Barry and City Administrator Elijah B. Rogers.

Dearborn, 47, also works as lecturer in public administration at Howard University and as a consultant on finance to the Urban Institute. His previous posts included financial director for the City of Cleveland, management analyst for the federal Office of Management and Budget and budget director of Fairfax County.