"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," Twardzik told MFC TV.
"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."
Twardzik goes straight into the Motherwell squad for Saturday's Scottish Premiership clash at Ross County.