The action came one day after Wingate cleared a final legal obstacle stemming from criminal and civil charges for rape and sexual assault in Maryland and San Antonio.
The contract covers the remainder of this season and two more seasons. Financial details were not disclosed.
The Spurs have one spot open on their 12-man roster because of an injury to Rod Strickland. The league must approve the deal and wants to discuss the situation with Wingate on Monday. He could be in uniform for Tuesday night's game against the Philadelphia 76ers in San Antonio.
"Our players and coaches have said that they would like to have David back on the team," said Bob Bass, the Spurs' vice president of basketball operations. "Last year, he added a dimension to our team, which is missing now.
"He can change the tempo of a game with his hustle and defensive skills."
Wingate's path back to professional basketball was opened Thursday by a Howard County state's attorney. William R. Hymes decided against trying Wingate on charges that he raped a 17-year-old girl last September in his Columbia apartment. Hymes said the alleged victim no longer wanted to press charges, even though she stated in court that Wingate raped her. The woman and her father said they did not want to pursue the case.
Earlier this month in San Antonio, Bexar County prosecutors dropped rape charges against Wingate in connection with a 22-year-old woman's claim that he sexually assaulted her last June. A civil case filed by the woman was settled out of court, and both sides declined to release or acknowledge any details of financial settlement.
Wingate was in the midst of contract negotiations with the Spurs when he was arrested. The team said it would not offer a new contract until all rape charges were settled.
Wingate could not be reached for comment. But after the Howard County case was settled Thursday, Wingate said he looked forward to resuming his NBA career.