"I wish him well," says Prokhorov.
NBA owners approved the sale of the Nets to the Russian billionaire last week.
Prokhorov says Wednesday he does plan to retain team president Rod Thorn.
New Jersey finished 12-70, the franchise's worst record and only the fifth 70-loss season in league history. Vandeweghe was the interim coach after the Nets fired Lawrence Frank during their 0-18 start, but was only expected to coach until the season ended.
On Tuesday, the Nets were forced to settle for the third pick in next month's draft despite having the best chance to win the lottery.