Gignac arrives at the club after nearly five years with the Ligue 1 side - for whom he scored 77 goals - and was welcomed by hordes of fans at Monterrey International Airport on Thursday as he flew in for his medical.
"Incredible welcome, thank you all, we're going to do big things," Gignac posted on Twitter.
He is joined at Estadio Universitario de Nuevo Leon by African attacker Uche, who has spent the last four seasons with Villarreal.
Uche scored 36 goals in his time with the Spanish club and posted on Twitter: "I'm very happy to announce an agreement with Tigres, I will do my best for the team #SomosTigres."
Tigres lost the Liga MX Apertura final to Club America late last year and, in 2015, their Clausura campaign ended at the quarter-final Liguilla stage at the hands of Santos Laguna despite topping the table after 17 matches.
However, Tigres are in the semi-finals of the Copa Libertadores - akin to the Champions League for South American and Mexican sides - and will face Brazilian side Internacional over two legs next month.
No Mexican team has ever won the elite continental competition since teams from the North American nation were first invited in 1998.