The talented playmaker has signed an initial two-year-deal with the Bantams after agreeing personal terms with the Yorkshire club.
The Saddlers exercised a year option in Osadebe's deal - having previously stated that talks with the Irishman were ongoing at the end of last season - in order to receive a fee from Mark Hughes' men.
“It feels great to finally have the deal over the line, as it has been going on for quite a while now, and I am just delighted to be here," said Osadebe.
“As soon as I spoke with the gaffer (Mark Hughes) and with Ryan Sparks, I knew the project was something I wanted to be a part of.
"We are all aligned in the same goals and this is the perfect place for me to take the next steps in my career.
“The manager we have has been at the top of the game and everyone at the club is driven in the same direction to achieve our goal of promotion, which we are more than capable of.
“Playing here in the past, it has always been loud, with the supporters imposing themselves on the game, and that is something I want to be a part of.
“Entertainment is a big part of my game. I want to get on the ball and make things happen, and am ready to kick on and do what I need to do.”
Osadebe leaves Bescot having made 81 league appearances across two seasons, scoring six goals, having mainly operated as an attacking midfielder.
Bradford boss Mark Hughes was delighted to get the signature across the line.
“Emmanuel is someone we have been tracking for some time, so we are delighted to be able to welcome him to the club," said the Bantams boss.
“He is another player at a great age, who has a lot of different components in his game which will certainly add to our threats as a side.
“His versatility and dynamism in the centre of the park and out wide - coupled with his determination to entertain people and be a part of something special here - made him a key target for us.
“I am sure you will join me in welcoming him to the club and, like myself, are looking forward to seeing him show us what he can do at Valley Parade.”
The enigmatic 25-year-old also had an impressive spell as a right-wing-back under Michael Flynn during the second half of 2021/22, but is expected to play further forward at Bradford.