The 41-year-old former Denmark and Celtic midfielder has signed a contract that will run through to the summer of 2014.
Erik Larsen has been assisting Laudrup this season, but he will now take on a greater responsibility for international scouting while Alan Curtis will remain as a first-team coach.
Wieghorst has been in charge of the Denmark Under-21 side, and will be allowed to oversee their two fixtures in March.
"I know Morten, I played with him, I coached him as a player and watched him as a manager," said Laudrup. "I had some inside information as my son Andreas has played for him.
"I wanted an assistant who had experience of being in charge as a manager, and he has experience of British football."
Wieghorst was at Celtic from 1995 to 2002, during which time he was diagnosed with Guillain-Barre syndrome before making a remarkable return to playing.
Wieghorst played alongside Laudrup in the Danish national side and was one of his former team-mate's first signings during his time as manager of native side Brondby.
Having moved into management he enjoyed successive Danish Cup triumphs with Nordsjaelland before taking over the Denmark Under-21 side.
He said: "Morten had a good playing career with Dundee and Celtic and the last years of his career he played under me at Brondby and won the league.
"He went to Nordsjaelland, who have been in the Champions League this season, first as an assistant and then as a manager, winning two cup titles which is huge for a smaller club.
"He has been with the Under-21 national team for the last year and a half."