The 49-year-old becomes the successor to Stephen Robinson after the former Fir Park boss resigned last week. He will be joined by long-time assistant Chris Lucketti and will inherit No.2 Keith Lasley as part of his backroom staff.
The former Scottish international is said to have impressed Fir Park bosses during the interview process and beat out former St Johnstone manager Tommy Wright and ex-Sunderland boss Simon Grayson. Lasley also interviewed for the role.
Alexander has experience of managing Fleetwood Town, Scunthorpe United and Salford City, as well as a role as caretaker of Preston North End, the club where he spent the majority of his playing career.
The 40-cap Scottish international will take over a side just one place above the bottom in the Scottish Premiership table. The Steelmen have failed to win any of their last 10 games in all competitions and were beaten by rivals Hamilton Accies 3-0 this past weekend.
Alexander told the Motherwell 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.”
Motherwell chairman Jim McMahon added: “We are delighted to have chosen Graham to be our next manager.
“The calibre of candidates for the role was high, as were the qualities shown by those we interviewed.
“Graham has demonstated to us he is the man to take us forward. He fits the profile of what we expect a Motherwell manager to be.
“He is dynamic. He is hungry. He will lead from the front and shares in our belief of developing talent. He also has a track record of success, leading clubs to promotions and cup finals.”