Arsenal is reported to have paid £12million to Chelsea to get a deal over the line in time, having failed in its attempt to bring in Moises Caicedo from Brighton and Hove Albion.
The Italy international provides another option for the Premier League leader in central midfield after losing Mohamed Elneny to a "significant" knee injury.
Jorginho revealed in his first interview as an Arsenal player that it was a transfer a long time in the making, with manager Arteta having tried previously to sign him.
"[Arteta] was a big influence. I know he tried a few times to get me before and it didn't happen due to other reasons, not because of my wishes," he said. "So of course, he had a big influence. Now I'm very excited for this new challenge, and I just can't wait to be on the pitch to be honest."
Jorginho boasts plenty of experience, having made more than 500 club appearances in his career and represented Italy 46 times.
Arsenal's interest in the Brazil-born midfielder only became public on Tuesday (AEDT) and he signed an 18-month contract at Emirates Stadium the next day.
"Everything has happened so fast. I was a bit surprised, but I took the opportunity of this amazing challenge," he said. "It's an important shirt. It's an amazing club, a big one, and I'm really excited and happy to be here.
"I'll try to just bring positive energy, hard work and my experience to help the team. It's what I always bring with me.
"I try just to help with the experience I've had in my time with the other clubs and anything I can do just to help the team to achieve more and more, that's my target.
"All I can promise is that I'm going to give my all to represent this club."
Jorginho has been handed the number 20 shirt and is in line to make his debut for Arsenal in the Premier League trip to Everton on Sunday (AEDT).