Vasseur, 54, joins Ferrari after spending the last five years with Sauber, who announced the Frenchman's departure earlier today.
Vasseur will step into the shoes of Binotto, who resigned from his role in charge of Ferrari's F1 operations at the end of last month. His official role will be team principal and general manager, starting on January 9.
"I am truly delighted and honoured to take over the leadership of Scuderia Ferrari as team principal," said Vasseur.
"As someone who has always held a lifelong passion for motorsport, Ferrari has always represented the very pinnacle of the racing world to me.
"I look forward to working with the talented and truly passionate team in Maranello to honour the history and heritage of the Scuderia and deliver for our Tifosi around the world."
"We are delighted to welcome Fred Vasseur to Ferrari as our team principal," added Ferrari CEO Benedetto Vigna.
"Throughout his career he has successfully combined his technical strengths as a trained engineer with a consistent ability to bring out the best in his drivers and teams. This approach and his leadership are what we need to push Ferrari forward with renewed energy."
Reports first emerged out of Italy ahead of the F1 season finale in Abu Dhabi that Binotto was set to leave the team and that Vasseur would take over.
Vasseur's arrival comes as part of Ferrari's push to end an F1 title drought dating back to 2008, having seen its early challenge to Red Bull this year ultimately fade through the second half of the season.
Ferrari will benefit from Vasseur's long career in motorsport that saw him co-found the ART Grand Prix junior team, which helped Lewis Hamilton, Charles Leclerc, George Russell and Nico Rosberg on their way up the ladder.
Ferrari driver Leclerc also made his F1 debut under Vasseur's stewardship at Sauber in 2018, and said in Bologna last week that he liked his management style.
"I've been working with Fred already from the junior categories, where he has believed in me, and then we've always had a good relationship," said Leclerc.
"But apart from that, obviously this shouldn't influence any of the decisions. He has always been very straightforward, very honest. And this is something that I liked from Fred."
During his time at Sauber, which has raced under the Alfa Romeo name since 2019, Vasseur helped turn the team around after years of financial strife and uncertainty.
The team enjoyed its best constructors' result in a decade this year as it finished sixth in the standings, as well as striking a deal to become Audi's works F1 operation when it joins the grid in 2026.