The Postal Board of Governors gave final approval Tuesday to a 3-cent increase in the cost of mailing a first-class letter, setting an April 3 effective date for the new 25-cent stamp.

The presidentially appointed panel approved the hikes, ranging from 13.6 percent for first-class mail to 25 percent for advertising bulk mail, in a private meeting and announced its decision at a news conference.The Postal Service estimates the new rates will add less than $10 a year to the average American's mailing bill.

A first-class stamp has cost 22 cents since February 1985, and the Postal Service plans to sell a transitional "E-Stamp" with a picture of Earth before it releases a new 25-cent version.

Under the new rates, third-class bulk advertising mail will increase by 25 percent, second-class mail for magazines and newspapers will advance by 18 percent and rates for postcards will rise by a penny to 15 cents.

A parcel post package weighing up to 2 pounds will increase from $1.19 to $1.63 and a 2-pound Express Mail package will edge up from $10.75 to $12.

The Postal Rate Commission cleared the major obstacle to the rate increases earlier this month, approving an average hike of 17.5 percent to offset a projected $5.1 billion deficit in 1989. The board had asked for the higher rates in May 1987, but approval from the commission was required before the panel could take a final vote on the hikes.

The Postal Service, reorganized along the lines of a private corporation in 1980, lost $223 million in 1987 after posting a surplus of $305 million in 1986.