The 22-year-old Mexican, who made his debut with the Swiss team in 2013 and had a mixed opening season, will partner German Adrian Sutil.
Russian Sergey Sirotkin, who Sauber had intended to promote, will be their reserve driver.
The 19-year-old, whose presence in the team is linked to an investment deal with Russian companies, was too inexperienced to earn an F1 licence.
Gutierrez's presence in the team is also linked to a continuation of Sauber's sponsorship deal with a Mexican telecommunications company.
Sauber's decision all but confirms that ScotPaul Di Resta has lost his place in F1 as only the two back of the grid teams, Marussia and Caterham, have yet to announce completed driver line-ups.
Marussia have already said that FrenchmanJules Bianchi will continue with them for a second season, while they will also retain Englishman Max Chilton, even though his seat has not yet been officially confirmed.
Caterham are assessing a range of drivers, among them their 2013 racers Charles Pic and Giedo Van Der Garde, Japanese former Sauber driver Kamui Kobayashi, Swedish GP2 driver Marcus Ericsson and the team's 2013 reserve driver Heikki Kovalainen.
Sauber team principal Monisha Kaltenborn described Gutierrez, who impressed on occasion in 2013, as "a talented young racing driver".
"Last season he experienced first hand how hard it can be for a rookie to step into Formula 1," she said.
"Nevertheless, throughout the season he improved significantly in qualifying as well as in the races and finished the year as the best rookie in the drivers' championship.
"Often the results didn't fully reflect his performances. I am confident Esteban will be able to use his experiences to gain results."
Gutierrez said: "It was a steep learning curve last season, but by working closely with the team I was able to improve continuously. It will be my fourth year with the team, the second as a racing driver, and I feel comfortable in taking the next step."
Of Sirotkin, Katenborn said: "He is taking the next step towards the top level of motorsport in his new role as a test driver. Our experience of him is as a very focused, calm and talented driver.
"Now we will continue to support him, including obtaining his super licence. Our goal remains to prepare him for a debut in Formula 1."