Gignac, Ligue 1's second highest scorer with 21 goals for Olympique de Marseille last season, arrived in Mexico on Thursday for a medical and to sign for Tigres, who face a Libertadores Cup semi-final against Brazil's Internacional next month.
"I'm very happy, I've come to win the league and the Libertadores," Gignac said on arrival in the northern city of Monterrey where Tigres are based.
"Incredible welcome, thank you all, we're going to do big things," Gignac said on Twitter.
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The 29-year-old Gignac, a member of France's 2010 World Cup squad, played for Lorient and Toulouse before joining Marseille that year.
Gignac arrived in Mexico the day after Uche and the pair could make their debuts for Tigres in the first leg of the team's Libertadores Cup semi-final away to Inter on July 15.
Uche, 31 and an African Nations Cup winner with Nigeria in 2013, has joined Tigres from Villarreal where he scored more than 30 goals in three seasons, having previously played for Recreativo Huelva, Getafe, Real Zaragoza and Granada.

Villarreal's Nigerian forward Ikechukwu Uche (2ndL) celebrates his goal during the Spanish league football match Levante vs Villarreal at the Ciutat de Valencia stadium in Valencia on November 24, 2013 (AFP)

Image credit: AFP

The Mexican 2015/16 Apertura championship kicks off on July 25.
Mexican team plays as guests in the Libertadores Cup, which went into a six-week break for the Copa America after the quarter-finals.
The closest a Mexican team has come to wining South America's top club competition was when Cruz Azul lost the 2001 final to Boca Juniors and Guadalajara lost to Internacional in the 2010 final.