And after a full pre-season with Newcastle United, the experienced defender says he's "ready to go" at Boro.
Targett is out of contract at Newcastle next summer so the 29-year-old will be determined to impress at Boro this season.
And his aim on Teesside is clear.
"I had a phone call with the manager and he was very honest with me," said the defender in his first club interview.
"The aim is to get this club back in the Premier League.
"I share the same ambitions. I'm coming here and hoping I can be part of a very successful team that leads this club back to the Premier League.
"I'm absolutely delighted to be here. The club has got off to a fantastic start, so I'm really looking forward to helping the team.
"I haven't played much football recently. I'm at an age where I want to play.
"When I found out Middlesbrough were interested, that was the club that I wanted to come to.
"The bonus is they've made a brilliant start in the Championship, so I'm looking forward to adding my experience and quality to the team."
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And Targett has plenty of experience. He's played 164 Premier League games and was a big hit for Newcastle in the early stages of his time on Tyneside after his £15m move from Aston Villa.
He needed hamstring surgery at the end of 2023 and then found himself down the pecking order after the arrival of Lewis Hall, while Eddie Howe also has the likes of Tino Livramento, Kieran Trippier and Dan Burn as left-back options.
Howe said last season: "I rate Matt very highly - I really do.
"Matt was a regular player for us (before injury). He'd done really well in our fight to stay in the Premier League."
Targett is now expected to go straight into the squad for Saturday's visit of Sheffield United as Rob Edwards' side look to extend their perfect start to the Championship season.
Targett said: "For sure I'm ready to go.
"I've had a full pre-season under my belt and haven't missed any training or games. I'm ready to go.
"I've watched some of the highlights [of Boro] and there's some really impressive play in there. I'm really looking forward to meeting the lads and joining in with them.
"And I'm looking forward to playing in front of the fans. I'm sure they're a very passionate bunch and the team is doing well, there's a real feel-good factor around the club at the moment."