The Whites filled their left-back vacancy by landing the signature of Firpo from La Liga giants Barcelona this week.
United parted with €15m plus add ons in the transfer while the Catalan club will hold a 20 per cent sell-on clause in any future sale.
Marcelo Bielsa and sporting director Victor Orta made a left-sided full-back their top priority this summer and have beaten a number of clubs to the signing of the former Real Betis man.
Serie A outfit AC Milan were among those to hold interest but Firpo will now link with his new team-mates at Elland Road.
Outgoing left-back Gjanni Alioski was a key part of the Whites' defence last season swapping with Stuart Dallas on occasion but the Macedonian will no longer be employed in West Yorkshire after failing to agree terms of a new contract.
Firpo, though, has taken up the number three shirt and looks set to solve Bielsa's long-standing problem of not having a natural first choice in the position in his senior squad.
“Look, we’ve been waiting for a long time,” Radrizzani told the club’s official site.
“Every week, I was expecting news from Junior’s agent and Victor. And finally, during the weekend, I got the feedback that he liked our proposal and he liked to join us, so we’re very happy and I think we put it out there an important element to continue to grow our club in what we deserve to be, and we’ll continue to grow, I’m sure about that.
“And as well for him, for Firpo, it is a fantastic opportunity for Junior to play with Marcelo because as you know he is a demanding coach, and also he will transform his career, I’m pretty sure about that.”