The former Liverpool midfielder was presented to fans and media on Monday.
The two went on to develop a strong working relationship before Rodgers was sacked in October 2015.
The swoop for Coutinho - which contains a 400 million-euro release clause - is the third biggest transfer in football history, outranked only by Paris Saint-Germain's world record 222 million-euro signing of Neymar from Barcelona last year, and their capture of French striker Kylian Mbappe for a deal eventually worth 180 million euros.
As for Coutinho, he addressed the Barca fans on Sunday ahead of his medical with the club, saying in a video message on Twitter: "Hi Barca fans, I am already here, it is a dream come true and I hope to see you tomorrow".
Coutinho's age is also highly attractive to Barca with Messi, Suarez and Iniesta all in their thirties.
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He's on about extending his contract but that isn't giving off the vibe that he wants to lay down roots in the city because he spends time in London throughout the week too.
He will be able to play in the Liga Santander, which his side lead by nine points from Atletico Madrid, and also the King's Cup knockout tournament, although an injury means he won't make his Barca debut until February.
Liverpool have been tipped to quickly reinvest their windfall from the Coutinho sale.
"We did everything within our means to keep Coutinho", said Jurgen Klopp, apparently with a straight face. At the time, Suarez was irreplaceable for Liverpool fans too.
"I have seen him play in various positions - on the right, the left, in the middle, on the wings". But when you let people go of that quality then you're going to lose some of what you do.
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"Our technical team, with Pep Segura and Robert Fernandez, have been saying for months that he was necessary".
They know it was coming to an end. And, of course, he was always going to get better physically.
One of the more interesting aspects is how he will fit in with Lionel Messi.
Barcelona then bought Ousmane Dembele from Borussia Dortmund for a deal that could reach 147 million euroe and Mestre said the club had been reticent to put themselves at financial risk.
'We had good period together in Premier League.
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