The 21-year-old German played for United’s youth side last year as an amateur and has now been rewarded with his first professional contract.
The Berlin-born player moved to Tannadice last summer from FC Hertha 03 Zehlendorf and impressed manager Jackie McNamara with his performances for the youth team.
Zwick, who had to overcome an initial bout of homesickness, said: “I have worked very hard to show my ability and I am delighted and proud to sign as a professional for United.
“My target is to now play games, continue my development and make an effort to secure the goalkeeper’s jersey for the first team.”
Goalkeeping coach Craig Hinchliffe said in a statement: “Luis fully deserves his contract. His story is fantastic and shows how determination and desire mixed with ability can achieve goals.
“He is an excellent technical goalkeeper. A modern goalkeeper if you like, fantastic with the ball at his feet and has proved he has the mental strength to succeed.
“He is one of three goalkeepers at the club who have the opportunity to prove they merit the first-team goalkeeper’s jersey.
“We have chosen to not give out the number one jersey because we have three goalkeepers all capable of playing in the Scottish Premiership and over pre-season, one will prove to me they deserve the jersey.”