The Buddies boss has shelled out an undisclosed fee to land his fellow Irishman on a one-year deal from Kilmarnock.
Goodwin was known to enjoy a tackle during his playing days and is looking forward to seeing Power add a combative streak to Saints in the months ahead.
"Alan is a very experienced central midfielder with a wealth of experience in the Premiership," Goodwin told the Paisley outfit's official website.
"He'll bring a real bit of steel to the middle of the park which we've lacked since I came back to the club.
"I feel we've missed that little bit of grit and someone who will go and make tackles and Alan will bring that in abundance.
"I'm really pleased with the work that we've done and I think it shows how hard we've worked from January onwards to get the business done as early as possible."
Power spent four years at Rugby Park after joining the Ayrshire side in 2017 following a six-season stint at Lincoln.
He also had spells down south with Nottingham Forest – where he made his senior debut in September 2007 – as well as Hartlepool and Rushden & Diamonds.
He becomes the fourth new face to check into the SMISA Stadium following the arrivals of former Killie team-mate Greg Kiltie, ex-Motherwell defender Charles Dunne and St Johnstone full-back Scott Tanser.
Power – who becomes the fifth Irish member of Goodwin's squad – said: "I'm glad to get it done and dusted.
"As soon as I heard there was interest I was pretty excited about it. St Mirren have been progressing over the past couple of years and I knew a good few of the lads.
"I spoke to Greg quite a bit and it made it a lot easier for me knowing a couple of the boys.
"The gaffer believed in me and hopefully I can bring all the things he wants me to bring to the club.
"The setup here is amazing and it's definitely a club moving in the right direction."