David Wagner’s side defeated Sheffield Wednesday 4-3 on penalties in the SkyBet Championship play-off semi-final second leg, after it finished 1-1 following normal and extra-time.
Keeper Danny Ward saved spot-kicks from Sam Hutchinson and then, crucially, from Fernando Forestieri to send his side through.
Wells won promotion to League One while at Bradford City in 2013 and the striker – who claimed Town’s equaliser – is hopeful ahead of his next Wembley date against Reading on May 29.
Wells said: “I’m not going to take anything away from how tough of a task it will be to go to Wembley and win.
“Reading are still on a high, but we fancy ourselves.
“We knew it was going to be tough (at Hillsborough), we knew the onslaught was going to be massive from them because they were at home but, over the two legs, we edged it.
“We created a few more chances, but most importantly we are going to Wembley.”
Steven Fletcher had converted a cross from Barry Bannan to head Wednesday into a 51st-minute lead but Town drew level 12 minutes later when a cross by substitute Collin Quaner was turned into his own net by Tom Lees under heavy pressure from Wells.
Wells said of Ward’s heroics: “Credit to the big man, he brought off some wonderful saves.”