Following his medical at City's Apperley Bridge training ground this Saturday, Vincelot has signed a two-year deal with the Bantams to become the club's seventh new arrival of the summer.
The Frenchman is not expected to feature in City's friendly with Burnley this (Saturday) afternoon but he is scheduled to be in the crowd at the Northern Commercials Stadium to watch his new team-mates in action.
The move is subject to the receipt of the usual EFL and FA clearances.
Speaking about Vincelot's move to the Bantams, McCall said: "We're delighted to get Romain into the football club.
"This is a deal we've been looking at for a while and Greg (Abbott) and Edin (Rahic) have worked well while we've been in Scotland to get this over the line.
"I see Romain fitting perfectly with what we want to do here. He has good experience of this level and his all-round game in midfield is very impressive.
"He can play the defensive role, he can be a box-to-box midfielder, and he can also chip in with the odd goal.
"I've spoken to a lot of people about him and having met him myself as well, you can tell he is a good character.
"He has a very strong desire and determination to do well for the club and I'm really pleased we've managed to bring him in."
Vincelot himself added: "I was very flattered when I first heard of the interest from Bradford as I know that this is a club with a lot of passion from the fans.
"I was excited by the prospect of joining the project here at Bradford.
"I knew of Bradford before I came to England due to their time in the Premier League. When I came to England and played against Bradford, I always found it a club with big passion and big crowds.
"It was always a good game playing at Bradford because you knew there would be a big atmosphere.
"The passion of the club and the passion of the fans really suits me and my game. I like to push myself to the limit in matches and I am sure the energy from the crowd will allow me to push that little bit more."
The 30 year-old joins McCall's squad with a reputation as being one of the most fiercely competitive and committed midfielders in Sky Bet League One.
Given his hard-working attitude and selfless displays, Vincelot can also fill in at right back and at centre half.
Vincelot was also deployed in an attacking midfield role on occasion for Coventry last season, however, netting four times during the 2015/2016 campaign for the Sky Blues.
Strong in the tackle, keen to challenge for the ball in the air, and with the ability to pass with both feet, Vincelot could easily be described as an 'all-action' midfielder.
Vincelot joined Coventry last summer after two productive seasons for the Frenchman with Leyton Orient.
He helped Orient to the League One Play-Off Final in his first full season at Brisbane Road, making 85 appearances in total for The O's.
Born in Poitiers, Vincelot began his professional career in his native France with Chamois Niortais and then Gueugnon, before moving to England to join up with Dagenham & Redbridge at the start of 2010.
He helped Dagenham to promotion via the League Two Play-Offs in his first season, playing in their 3-2 final victory over Rotherham United at Wembley.
By the end of his first full season with Dagenham - the 2010/2011 campaign - Vincelot was the Daggers' top scorer with twelve goals.
His impressive form with Dagenham led to a move to Brighton & Hove Albion in the summer of 2011.
Vincelot spent a season and a half with the Seagulls, enjoying a brief loan spell with Gillingham during his period, before moving to Orient in 2013.