"He's going to start," Vogel told reporters. "We will keep an eye on his minutes. I don't know exactly what that's going to look like."
The two-time All-Star and four-time NBA rebounding champion is averaging 17.5 points and 13.5 rebounds per game this season. Drummond appeared in 25 games this season for the Cavaliers, but hasn't played since Feb. 12. The Cavaliers took him out of their lineup as they looked for a trade partner, but eventually agreed to the buyout.
Drummond had his first full practice with the Lakers on Tuesday.
"He appears to be in very good shape," Vogel said. "It's clear that he has worked really hard during the time he has been off."
Gasol, 36, has averaged just 4.8 points, 3.9 rebounds and two assists per game in 38 starts this season. Backup center Montrezl Harrell has averaged 15.2 points and 6.8 rebounds per game off the bench for the Lakers.
Lakers forward LeBron James has missed the last five games due to a high ankle sprain. He isn't expected to return until at least late April. Fellow Lakers All-Star forward Anthony Davis has missed the team's last 19 games due to a calf strain and tendonitis in his right leg.
"I think the level of excitement for me is at an all-time high," Drummond told reporters Tuesday.
The Lakers and Bucks tip off at 10 p.m. EDT Wednesday at Staples Center. The Lakers then have a stretch of seven-consecutive road games from Friday through April 13.