The couple are looking at a summer wedding in France, where Parker is from, Anderson told the San Antonio Express-News.
Anderson reportedly said that Parker flew to Los Angeles after the Spurs game in Utah on Wednesday and surprised Longoria by proposing at her home.
"It was very romantic. Evidently he went down on one knee," she said, adding that the "Desperate Housewives" star said yes to the proposal "very happily."
Parker called his father Thursday to let him know his plans.
"He did this all on his own," Tony Parker Sr. said. "I had actually thought it might happen sooner, but he caught me off-guard. I'm very happy for him."
Longoria broke the news in a call to Ryan Seacrest's radio show on KISS-FM, Los Angeles.
"I always promised you that you would hear it first and here we are. I wanted to tell you that Tony and I are engaged," Longoria said on the air.
Couple mistakenly served bag of cash at McDonald's drive-thru
Beyonce flaunts bikini body, Blue Ivy in vacation pics