The hosts ran in five tries to secure their 12th victory in last 13 league matches, with 37-year-old centre Jimmy Gopperth finding the target with nine of his 11 kicks for a 22-point haul.
Lee Blackett's side will face table-toppers Exeter Chiefs, who beat fourth-placed Bath, at Twickenham, with the showpiece event scheduled for 24 October.
Wasps raced out of the blocks to take the lead inside 10 minutes after a beautifully-weighted chip from Dan Robson found centre Malakai Fekitoa, who finished from close range.
Gopperth added a further two penalties to hand Wasps a 13-0 lead before the visitors got on the scoresheet, with Luke Morahan finishing off their first attack at the Ricoh Arena. Another penalty and a try from the influential flanker Jack Willis saw Wasps hold an 18-point advantage at half-time.
Harry Thacker pulled one try back for Bristol early in the second half before Robson, Zach Kibirige and Matteo Minozzi went over late to seal a comfortable victory for Wasps.
Wasps have claimed the Premiership title on six previous occasions, last lifting the trophy in 2008.
"I can't tell you how hard we've worked to get here," said Willis, who was man of the match. "I think the first half of the season was frustrating for us. "It's been so special what we have done since the lockdown and we can't wait for the next couple of weeks."
It was a day to forget for Pat Lam's Bristol, who had reached the playoffs after recording their highest points tally in a regular top-flight season.
"We made it tough on ourselves," he said. "This doesn't take away from the effort of the season, but unfortunately we have to take some of these hits on our journey. It's certainly one of the games that will make us stronger."
Bristol can still finish the campaign with silverware as they face French side Toulon in the European Challenge Cup final at Stade Maurice David in Aix-en-Provence on Friday.
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