The 25-year-old marksman completed the formalities of his switch on Monday evening and reported for training for the first time at Rockliffe on Tuesday.
"It's nice to be here," said Rhodes. "It's been a hectic few days, but it'll all be worth it.
"I'm looking forward to bedding in and settling down and getting to know the players, the fans, and everyone in the area."
Rhodes arrives with the reputation as being one of the most prolific goalscorers in the Football League in recent seasons.
He bagged 40 in 2011/12 to help Huddersfield win promotion, broke record after record with the Terriers, and continued to prove destructive in front of goal after an £8m move to Blackburn.
"It's something that I enjoy and live for doing but it's not a matter of who scores," said Rhodes.
"It's about scoring more goals than the opposition and picking up the points to get to the place where we want to go.
"I'll give my all and work as hard as I can. I can't guarantee anything but I'll work as hard as I can to make myself a better player and a person to do well for this club."
Rhodes has been linked with the club on previous occasions, but he says he won't be taking anything for granted, following his arrival on Teesside.
"It's taken some time to get here," he said.
"There's an overwhelming desire to have people who want you and I'm looking forward to getting started.
"Middlesbrough is a fantastic club with a fantastic team that has been doing well this season.
"It's a really good team, and a squad of players. Nothing is taken for granted, and whenever the manager calls upon me I will be trying my best to play my part."
WATCH: See all Jordan Rhodes goals this season
FACT FILE: Everything you need to know about Jordan Rhodes