Milwaukee also added guard Justin James in the deal.
Bogdanovic, 28, has averaged 13.5 points, 3.5 assists, 3.2 rebounds, and a steal with 37.4% 3-point shooting in three NBA seasons.
Bucks general manager Jon Horst has acted aggressively in the opening days of player movement. He also added All-Star guard Jrue Holiday from the New Orleans Pelicans in a trade that sent three first-round picks and two rotation players in Eric Bledsoe and George Hill to Louisiana.
DiVincenzo averaged 9.2 points, 2.3 assists, and 4.8 rebounds in 66 games last season. Ilyasova put up 6.6 points and 4.8 boards across 63 contests, while Wilson has made sporadic appearances during his three seasons in the league.