The Northern Irishman signed a 12-month rolling contract with the Hoops this past week in what is a major statement of intent by the club's board, given his history.
It is the 43-year-old's first job in management since being sacked by Liverpool in October, after three-and-a-bit years at Anfield in which he came within a point of delivering a Premier League title back in 2014.
Joining the Bhoys may be considered a step down, but Rodgers revealed during the press conference for his unveiling that he is a boyhood Celtic fan and simply could not turn down the chance to manage the Hoops.
Mulgrew, 30, is technically without a club after his contract with Celtic expired, but the Scottish centre-back says that the chance to work under Rodgers has only made him more desperate to be offered a new deal by the club.
“Last week, when Brendan Rodgers was named as manager, I just thought, ‘wow'," he said to The Scottish Sun.
“I wanted to stay at Celtic before I knew he was taking over but his appointment only made me more desperate. Obviously his name had been linked with the job for a while but I didn’t think it was going to be possible to get him.
“But he’s here and I think he’s just what Celtic need. It’s exciting times and his arrival is a huge scalp for the club."
New Celtic manager Brendan Rodgers with the Scottish Premiership trophy after the press conference