The club's previous record fee was 55 million pounds paid to Wolfsburg for midfielder Kevin de Bruyne in 2015.
"I am very happy to be here," Laporte said in a club statement. "City are a club with a lot of ambition and they are one of the best teams in Europe.
"I am looking forward to working under Pep Guardiola and trying to help the Club to achieve success.
"It means a lot that the Club have shown faith in me and I am excited to get started."
City coach Guardiola wanted to add another centre back to his squad to challenge Nicolas Otamendi and John Stones with ongoing injury concerns surrounding captain Vincent Kompany.
Laporte, a left-footed defender, was a first-team regular at Bilbao since breaking through in the 2012-13 season and he helped them win the 2015 Spanish Super Cup. He clocked up a total of 222 appearances for the Basque club, scoring 10 goals.
On the international stage, Laporte has featured 19 times for France at Under-21 level.
Laporte becomes City's sixth signing of the season following the arrival of Ederson, Danilo, Kyle Walker, Benjamin Mendy and Bernardo Silva at the start of the campaign.
Speaking at a news conference ahead of Wednesday's league clash against West Bromwich Albion, Guardiola said Laporte has all the attributes required to adapt to the demands of the English game.
"We are very aware of his skills. He's an experienced central defender on the big stages and has the skills to help us," Guardiola said.
"He will be able to start right away. The Premier League is special in many senses. But he is intelligent.
"It's always tough for a new player but we will be patient with him. He is the perfect age to be with us for a while."
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond and Christian Radnedge)
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