Ealing, meanwhile, will remain in the second tier next term as the play-offs were scrapped in favour of automatic promotion for the league winners.
Head coach Lam told BBC Radio Bristol: "I'm extremely proud, for all the players, the management, the staff, the board, the Lansdowns and all Bristol people.
"Although people say it was a formality, you have to work hard for it, so I'm pleased that we're heading up and we continue on the journey towards getting Champions Cup rugby.
"This is only part of the journey, it's only the first step. We've just done the first part but there's a long way to go to get where we want to get to."