"We are engaged and are both really happy," Vujacic said Thursday night before the Lakers' exhibition game against Golden State. "It's good and now we can focus on other things."
The agent for three-time Grand Slam champion Sharapova confirmed the news in an e-mail to The Associated Press.
Vujacic said he proposed on the one-year anniversary of their first meeting at a friend's barbecue.
"It's was probably old school," Vujacic said. "I had to do it like a gentlemen."
Vujacic said a wedding date hasn't been set.
The Slovenian guard returned to action Thursday, a week after getting a concussion when teammate Lamar Odom accidentally elbowed him in the face during practice. Vujacic averaged 2.8 points and 1.2 rebounds in 67 games for the Lakers last season, his sixth with the club.
Sharapova won her first major title at Wimbledon in 2004, when she was 17. She went on to win the 2006 U.S. Open and 2008 Australian Open and also reached No. 1 in the WTA rankings.
After shoulder surgery and an elbow injury forced her to miss time the past two seasons, Sharapova is currently ranked 18th.