The Blues manager says he is sure his and the owners' ambition means success could be on the horizon.
Redknapp has signed a one-year contract to continue at the Blues helm.
He took over on an interim basis for the final three matches of the campaign and steered Blues to Sky Bet Championship survival.
"I really enjoyed the three weeks I had here, I got a real buzz, so it was an easy decision for me to make," Redknapp told bcfc.com.
"The sell out 28,000 crowd in that Huddersfield Town game, the way the players responded and performed, there's great people around the Club.
"I just thought 'let's see if we can put together a competitive team and have a go at it at the other end of the league'.
"And I think we can. You know, it reminds me of Portsmouth in my first year: they were struggling at the bottom of the Championship, we put together a team in the summer and I didn't really know what to expect - but we ended up winning the league.
"If we can turn things around like that here, in a similar kind of way, then it would be fantastic, but I know it's a big challenge."
Redknapp says Blues owners and Board of Directors certainly did their bit to effectively bring him out of retirement.
"Without a doubt, the owners are ambitious people, they want to take the Club forward," he said.
"There's lots happening. We've got a new pitch being laid in the summer, we've got great facilities at the training ground and of course they're going to be providing backing to bring players in as well.
"It's a tough job, a big challenge in this league, but if we can do things right and bring in good players to go with the good players we already have here, then we could have a chance."
Redknapp added: "I'm looking forward to it. This is a big club, a proper club, fantastic supporters, proper people. There's lots to do over the summer and I'm sure we will all give it a go."