Stanford men, who had a 3-2 record, had a 7-4 mark entering the final weekend of March and ended the week 3-0.
Goolsby, a 6-foot-5, 200-pounder from New Jersey, averaged 15.4 points and 4.3 rebounds in 24 games with the Cardinal last season.
He averaged 6.3 points and 5.3 assists for the men last season, and he had eight double-doubles, a double-double and a team-high 17 blocks in 15 games.
The team is also signing guard Kameron Wilkerson, a five-star prospect from New York who had offers from Duke, Michigan State and Notre Dame, to a multiyear deal, a source told ESPN.
The two-time All-American was the leading scorer for the Stanford men last year and led the team with eight assists.
He averaged 12.5 points, 3.5 assists and 2.2 steals per game.
The Cardinal were ranked No. 1 in the preseason and have now dropped seven of their last eight games, including a 20-13 loss to UCLA in the Pac-12 Tournament semifinals.