The 22-year-old hot-shot became Rovers' record signing when he completed an £8m move from Huddersfield Town on Thursday following a transfer chase that has lasted most of the summer.
Rovers had three bids for the Scottish international turned down before a final one was enough to make Rhodes the club's ninth new arrival of a busy summer at Ewood.
"I've known of the interest from the start of the summer," revealed Rhodes. "Bids were made, bids were turned down, but the club persisted.
"It just goes to show how much the club and the manager wanted me here and that is a really good feeling to have somebody want you so much in their side and to want you at their club.
"I'm delighted to just be here. When you look around at all the facilities and the players in the dressing room and everything it is just fantastic to be a part of.
"I can't wait to just get started here really, hopefully it will be tomorrow against a tough Leeds United side, it would be great to go there and get the three points."
Tickets for Saturday's Leeds United match will be available on the day of the game from Elland Road. Prices are £36 for Adults, £24 for Seniors 60 and over, and £17 for Juniors aged 15 and under.
For those supporters who are unable to go, Rovers Player
will be providing full uninterrupted commentary of the match from 2.45pm.