Bell, a much-loved figure among the Rangers players and backroom staff, died suddenly on Tuesday to cast a pall over the build-up to Thursday night’s momentous fixture.
Tavernier scored the first goal as Rangers beat Leipzig 3-1, clinching a 3-2 aggregate victory and a place in the Europa League final against Eintracht Frankfurt in Seville on May 18.
It will be Rangers’ fifth appearance in a European final and their first since Smith, who passed away last October, guided them to the UEFA Cup final in Manchester in 2008.
“First and foremost we wanted to do it for Jimmy, and I’m super proud of the effort all the lads put in and all the staff and all the fans,” said an emotional Tavernier.
“He will be looking down proud - so will Walter on all of us - it’s for them. I’m absolutely delighted.
“We are through to the final. Unbelievable. It was a tough test but an unbelievable feeling to be in a European final - it’s what you dream of.
“We wanted to come here with a result (from the first leg) we could work with, which I thought we did. You saw the first couple of minutes how we set out, the pressure and how we got in their faces, making it hard for them. The boys executed it to a tee. I’m buzzing.”
Tavernier now has the opportunity to become only the fourth player to lift a European trophy as captain of a Scottish team after Billy McNeill (Celtic 1967), John Greig (Rangers 1972) and Willie Miller (Aberdeen 1983).
“We will go there full of confidence,” he added. “We have got into the final for a reason. It’s one game and we will give it everything like we did tonight.
“We want to win it. We are in this competition to win, we are a club that wins trophies and that’s what we want to do.
“We want to make all the fans proud. We will be taking lots of fans over to Seville and it will be great scenes.”