The Chile midfielder was close to joining Inter Milan, but Barca made their move when the Serie A side turned their attentions to Luka Modric.
Barcelona hope Vidal, 31, will fill the void left by Paulinho, who has returned to Chinese club Guangzhou Evergrande after a single season at Camp Nou.
Barcelona had been in discussions to sign Adrien Rabiot only to move for Vidal when it became clear Paris Saint-Germain had little interest in selling the France international.
Before their capture of Vidal, Barca had spent more than £100m to bring in French defender Clement Lenglet and Brazilian pair Arthur and Malcom.
The Brazilian recruits have already made a telling impact. Arthur scored on his debut, a long-range effort against Tottenham, before Malcom netted against Roma on his first start.
Roma were expected to sign Malcom before Barcelona launched a successful late swoop for the youngster.