Alexander succeeds another former PNE player in the Fir Park hotseat, Stephen Robinson having stepped-down from the job on New Year's Eve.
Him and Robinson were team-mates at North End for a time.
The 49-year-old's first task will be to guide Motherwell away from relegation danger, with them currently second from bottom of the Scottish Premiership.
Motherwell are the fourth club he has managed full-time, after stays with Fleetwood Town, Scunthorpe United and Salford City.
He was sacked by Salford earlier in the season despite them being unbeaten in League Two and sitting high in the table.
Alexander's first experience of management came at North End where he was joint caretaker boss with David Unsworth between the sacking of Phil Brown and Graham Westley's appointment.
He made 421 appearances for PNE in two spells, the bulk of those between March 1999 and August 2007.
After four years at Burnley, Alexander returned to Deepdale at he start of the 2011/12 season, his final game as a pro seeing him score a stoppage-time free-kick against Charlton Athletic.
At Motherwell, Alexander will have former North End skipper Chris Lucketti as his assistant.
Alexander told Motherwell's official website: "I am delighted to have been handed this role at a great club.
"People will get to understand the hard work I put in, along with my staff and players. I have always brought that to every club, as a player and a manager.
"It’s something different. It is something I am really excited about. I have been a manager now for seven to eight years, and had success with the three clubs I’ve been at. But this is out of my comfort zone. I’m someone who is up for a challenge, and I will get that here.
"I spoke to Stephen Robinson, as we played together at Preston. He said nothing but good things. That together with what I heard from the board meant it was a challenge I wanted to take on.
"The obvious first objective is to win on Saturday. This is a team which is underperforming but there is talent there. We are in a month where we can also make additions, but there is no way I see this current group should be where they are.
"I believe in producing young talent and I’ve always given chances. The board have made clear what they see as success for Motherwell, and I want to exceed those expectations.
"I’ve seen if you work hard enough, you can achieve whatever you want. But the work has to go in. And that not only comes from me, it comes from the whole group. My role is a manager is to get that working straight away."
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