The Mexican has started 38 races in two seasons in Sauber's line-up, but registered just one points finish - placing seventh at the 2013 Japanese Grand Prix.
Sauber struggled for pace throughout 2014 and failed to pick up any championship points between Gutierrez and team-mate Adrian Sutil.
A 12th-place finish in the season-opening Australian Grand Prix was as good as Gutierrez's season got, and he confirmed his intention to leave the team ahead of the Brazilian Grand Prix in November.
Gutierrez is the second driver to move to Ferrari after four-time world champion Sebastian Vettel's switch from Red Bull to join Kimi Raikkonen in the Italian manufacturer's main line-up.
"It is an honour to become part of the Scuderia Ferrari family, a team with such an exceptional history," Gutierrez said.
"It is for me the beginning of a new path for my future and I'm going to do my utmost to contribute to the achievement of the targets set by the Scuderia.
"I want to thank everybody for their belief in my potential; this will bring a great opportunity for me to develop further and get to the top in the near future.
"With all my passion and dedication, I'm now looking forward to the start of this new venture."