The pair have moved to the Ricoh Arena as manager Mowbray continues to revamp the club since signing a two-year deal last month.
Former Wolves defender Venus is the Sky Blues’ new technical director while ex-Birmingham and Ipswich full-back Clapham has been appointed to assist Mowbray with coaching the first team while also taking the under-21 squad.
The duo also worked with Mowbray at West Brom and Middlesbrough.
Mowbray said: “Throughout my discussions with the club’s owners and the board, the main areas I highlighted were the structure and the recruitment at the club.
“If we’re going to achieve our aims and ambitions, it is important not to just focus on the pitch but also the work we do off it.
“If you look at the work I did at Middlesbrough and West Bromwich Albion, there is now a successful structure in place at those clubs and this is what I want to replicate here.
“Mark is someone I’ve worked with for many years and have enjoyed a lot of success with, and Jamie has impressed me with his coaching skills and development during my time at Middlesbrough.
“These appointments are hopefully the first of many steps to bringing this club forward and pushing for a successful 2015/16 campaign and beyond.”