Giannis Antetokounmpo top-scored with 20 points as the Bucks won 116-91 on Wednesday to make the final four for the first time since 2001.
They face the winner of the Toronto Raptors versus the Philadelphia 76ers, with the Raptors currently 3-2 ahead.
Meanwhile, the Golden State Warriors are one win from the Western final.
Milwaukee, who had not won a play-off series against the Celtics since 1983, dominated games by nullifying the threat of Kyrie Irving.
Irving, who shot one-for-seven from the three-point range and finished with just one assist, will become a free agent this summer.
Golden State took a 3-2 series lead against the Houston Rockets thanks to a 104-99 win in game five of the semi-final.
The Warriors lost Kevin Durant to a calf injury in the third quarter but saw Klay Thompson finish with 27 points and Stephen Curry make 25.
The defending champions could set up a sixth successive appearance in the Western finals when they face Houston in game six on Friday.
They would then face the winner of the other Western semi-final between the Portland Trail Blazers and the Denver Nuggets, with the Nuggets holding a 3-2 lead.