A Rosslyn office tower was approved by the Arlington County Board yesterday after the developer offered $3.5 million for low-cost housing and road improvements and promised one floor of the building for a day care facility.

The 13-story building will house the national offices of the nonprofit Gannett Foundation and will be third structure in a development that includes the twin 23-story office towers that serve as headquarters for USA Today and the Gannett Co. Inc.

In making the unanimous decision, the board reversed its land use policy that required a residential building on the site.

The board's action also closed a chapter in the development of Rosslyn.

The building at 1101 Wilson Blvd. will be the last such building approved for Rosslyn, said board member Ellen M. Bozman. There are other open sites in the area, but they have building plans that have been approved by the board.

The board on a split vote also approved a sign reading "Gannett Foundation" for the building even though there were concerns that the sign, which exceeds county standards, would be visible from the national monument area of Washington.

The contribution was announced at the board meeting by William G. Brakefield, general partner of 1101 Associates, the developer.

County Board members were informed of the offer Friday: If the board allowed construction of an office building rather than a hotel, as originally planned, the developer would contribute $2.5 million to the county for a low-cost housing fund, Brakefield said. Another $1 million would go toward construction of a loop road in Rosslyn, he said.

The contribution is "certainly the largest cash donation" ever from a developer, said County Manager Anton S. Gardner.

Members of the board's Democratic majority were particularly vocal in defending their decision to overturn a longstanding policy regarding the site.

Board Vice Chairman John G. Milliken said he was eager to have the Gannett Foundation move its offices from Rochester, N.Y., to Arlington because it has a reputation for supporting causes in its home community.

More than half the foundation's annual grants go to charitable causes in communities served by the Gannett newspaper chain, said its president and chief executive officer, Eugene C. Dorsey.

County Board Chairman Albert C. Eisenberg praised the developer's offer of money for housing and roads and the child care facility.

"You have to look at the benefits," he said. During his recent campaign for reelection, he had boasted of his toughness with developers.

Eisenberg also had criticized Jane Bartlett, a Republican-backed challenger, who as a member of the Planning Commission in 1984 had supported a third office tower on the site.

At that time, the same developer had offered several million dollars for transportation improvements.

Yesterday he took pains to point out that the building he voted for is "much lower, much smaller" than the one proposed and defeated three years ago.

Bartlett said yesterday that she had no quarrel with the board's approval of the building.