The Chilean enforcer was announced as the Catalan side's latest signing, pending a medical, on Friday night, following a three-year spell at the Allianz Arena, during which he helped the Bavarian giants conquer the Bundesliga for three consecutive seasons.
Vidal is believed to have joined Barca for around £27m and has signed a three-year deal with the current La Liga holders.
One of the most successful players to ever hail from Chile, the 31-year-old also won four league titles with Juventus in Italy. Vidal has won a league title every year since 2012 and will hope to carry on with the trend with his new team at the end of the upcoming season.
Per El Chiringuito TV, United and City both opted to pass on the player when he was offered to them for £27m. The player's age and a history with knee issues, particularly two surgeries, are credited with their refusal.
"Arturo Vidal was offered one month ago to Manchester City and Manchester United by his agents but both clubs discard the offer," journalist Jose Alvarez tweeted on Saturday morning. "His age and his knee [two surgeries] were the reason of the refuse even the price was reasonable."
Both Manchester clubs are understood to be in search of a new midfielder this summer, more so City, who missed out on signing Jorginho last month due to interference from Premier League rivals Chelsea.
The English champions had a deal in place to sign the Brazilian, but the Blues managed to hijack the move and have since gotten the player on their books.
The Red Devils could also be in the market, given the uncertainty surrounding France international Paul Pogba, who is rumoured to be itching for a return to Juventus.