Scripps Howard Broadcasting Co. announced yesterday that it had completed its purchase of WMAR-TV (Channel 2) from Gillett Broadcasting for $125 million.

As part of the closing, Gillett dismissed a breach of contract lawsuit it had filed after Scripps Howard terminated in February an agreement reached last year to buy Channel 2 for $154.7 million, Cincinnati-based Scripps said in a statement.

The parties announced in March that they had reached a tentative pact for the sale of the station and dismissal of the suit. They came to a final agreement early last month.

Arnie Kleiner, president and general manager of Channel 2, said he expected an "easy transition" to the new ownership. He said that he anticipated no changes in the operation of the station and that he "absolutely" intended to remain in his position.

Mr. Kleiner said the station was "very fortunate" to have been purchased by Scripps Howard, which he said is "in the broadcast business to stay."

Greg Hartel, Scripps Howard's manager of corporate communications, said that the company would have no comment beyond a brief statement announcing the closing of the sale.

Gillett purchased WMAR and a UHF station in Richmond, Va., from the Times Mirror Co., the parent company of The Baltimore Sun, for $209 million in July 1986. At the time, WMAR was valued at $190 million.

In addition to WMAR, Scripps Howard owns nine television stations; cable systems serving about 270,000 basic subscribers; and five radio stations, including WBSB-FM (B-104) here.