The 21-year-old – son of World Cup winner and France great Lilian Thuram – has penned a four-year contract with the Bundesliga side.
Thuram joined Guingamp in 2017 from Sochaux and scored 17 goals in 72 appearances across all competitions for the French side.
Nine of those goals came in Ligue 1 last term, but they did not prove enough to stop Guingamp from being relegated to the second tier.
Thuram then spent the summer representing France at the Under-21 European Championships, where they were knocked out at the semi-final stage by eventual champions Spain.
"We're thrilled to have Marcus on board," said Monchengladbach's sporting director Max Eberl in a statement.
"He is a fast, robust and dangerous attacker who fits into our squad well. We’re confident that he will make his mark in the Bundesliga."
Thuram joins a Gladbach side that finished fifth in Bundesliga last season - three points off the top four and Champions League qualification.
Borussia Monchengladbach have announced the signing of Marcus Thuram, son of Lilian. 🤝— Goal (@goal) July 22, 2019
Here's what the striker can do! 🔥pic.twitter.com/dODjJPo1lj
That secured them a Europa League spot for the upcoming campaign, though they head into the new season reeling from the departure of star player Thorgan Hazard.
But he formed part of Dortmund's aggressive early-summer spending spree, joining Julian Brandt, Nico Schulz and Mats Hummels in moving to Westfalenstadion.
Gladbach kick-off the new Bundesliga season against Schalke on August 17, though their first competitive fixture comes eight days earlier when they face Sandhausen in the first round of the DFB-Pokal.