They surpassed the previous record of 263-5, set by Royal Challengers Bangalore in 2013
The 28-year-old Croatia international has won two La Liga titles, two King's Cup trophies and a Champions League crown with Barca since joining from Sevilla in 2014 for an estimated 20 million euros and will sign the new deal, which the club said has a release clause of 125 million euros, on Friday.
Rakitic was left out of the starting line-up in the 4-0 defeat by PSG in the first leg of their Champions League last 16 tie but he played an important role in Wednesday's drubbing of the French champions.
"It's unbelievable, we made the impossible possible," Rakitic said in an interview with CNN on Thursday.
"It's really hard to explain what happened yesterday; I think it was a crazy night, a crazy match and I'm so proud to be part of this team."