The Scots prop up the rest of Group A after taking just two points from their opening four games - a run of results that ultimately cost Craig Levein his job in November.
Speaking as the new national team boss was presented at a media conference at Hampden, Regan said: "Gordon has got a series of duties set out within his contract. It's not really appropriate to go into what they consist of but ultimately his challenge is to start to move Scotland up the group table for the Brazil 2014 campaign."
The national team's chances of defying the odds to book a place at Brazil in 2014 have been written off in most quarters, although Strachan's own response to that question on Tuesday was: "We'll give it a go."
He takes charge of his first match against Estonia in a friendly at Pittodrie on February 6, before Scotland face Wales and Serbia in a qualification double-header in March. And Regan has backed Strachan to make sure the campaign does not end in humiliation.
"We would like to avoid finishing last," Regan said. "He more than anyone wants to make sure that happens. Also, it's about preparing for France 2016. Gordon is keen to develop a format of play, a philosophy, if you like, for the Scotland team that works. We're backing him to do that."
Strachan has managerial experience at club level with Coventry, Southampton, Celtic and Middlesbrough. He also boasts a playing career that included spells at Aberdeen, Manchester United, Leeds and Coventry, as well as 50 caps for Scotland.
Regan added: "As a player, he experienced what every Scotland player wants to experience - participating in a major tournament. He can share those experiences with the squad as we prepare to qualify, hopefully, for France 2016.
"Gordon has had experience as a manager at club level and has experienced participation in the Champions League and has also experienced winning a major tournament, the FA Cup final, in England.
"Gordon's network in football is second to none. Finally, the single biggest factor that inspired the board, was Gordon's passion and his desire for the job. He made no secret of wanting this job. He's really worn his heart on his sleeve in terms of wanting to be Scotland manager."