The Seattle City Council unanimously approved Tuesday an agreement clearing the way for a dramatic makeover of Yesler Terrace, which opened in 1941 as the city’s first public-housing project. The agreement allows high-rise buildings up to 300 feet at Yesler Terrace, just south of Harborview Medical Center on First Hill. The Seattle Housing Authority, which owns Yesler Terrace, plans to sell some of its 30 acres to private developers who would build office, condo and apartment towers on the property. The housing authority hopes to use $145 million from property sales to rebuild Yesler’s 561 well-worn apartments, along with streets and water and sewer lines. Residents would be relocated during phased construction that could take up to 20 years. The council also required the housing authority to use all proceeds from the sale of land for rebuilding Yesler Terrace. If the authority gets more than it needs, the money will be used to pay for up to 100 additional apartments for low-income residents.