Gunnar Nielsen has been deputising since Lee Hollis suffered an ankle injury but the Faroe Islands international is a doubt for Saturday's Scottish Premiership clash at Ross County after picking up a thigh problem during the 5-0 defeat by Celtic last Friday night.
Under-20s goalkeeper Ross Stewart is the only fully-fit goalkeeper at Fir Park as teenagers Max Currie and Brett Long are also ruled out so Twardzik goes straight into the squad for the Dingwall clash.
The 22-year old, who is the brother of Celtic twins Filip and Patrik, almost signed for Motherwell in 2009 but ended up at Karlsruhe and joined Dundee via Aberdeen after leaving Italian side Como in January.
Twardzik told MFC TV: "It has been a whirlwind last 24 hours, it's hard to believe how quickly things came about. I am desperate to help Motherwell out and hopefully I can.
"I was here in 2009 in pre-season. I tried to get away from Bayern Munich but they tried to get compensation and I had to leave Motherwell. I'm happy to be back, even if it's only for a couple of weeks."
Manager Stuart McCall added: "Gunnar Nielsen picked up a knock in his thigh against Celtic and is a major doubt for the game on Saturday.
"We are grateful to Dundee for letting him come out on loan to us. I spoke to John Brown, who speaks very highly of him, and he would certainly be knocking on the door but for the form of their number one, Kyle Letheren.
"Gunnar is improving every day and we'll give him every chance of being fit but in the worst case scenario, at least we can go there with two fit goalkeepers."