The 58-year-old, who will leave his England post, has managed Bournemouth, Doncaster Rovers, Crawley Town, Nottingham Forest and Bristol City.
Reds academy coach Pep Lijnders joins the first-team staff, with talks continuing over a third new coach.
Manager Brendan Rodgers needed replacements after the sackings of Colin Pascoe and Mike Marsh.
He said: "I have made these appointments because I want to take us in a new technical direction, in terms of coaching.
"I believe the entire first-team set-up will benefit and I am extremely positive and excited about what we can achieve, as a group, going forward.
"My admiration for Sean, as a professional, is well documented. He is someone with a clear vision and philosophy and has proved he has the ability to transfer that knowledge, through his coaching, to the players."
O'Driscoll, who had only been England Under-19s head coach since September, added: "I am excited to be joining one of the world's most iconic football clubs.
"The hallmark of any successful club is its culture and that comes from the people who work there, from the chief executive and first-team manager to those people behind the scenes whose faces may not be known but who are the lifeblood of the club."
The majority of Liverpool's players have reported back for pre-season training to be greeted by the revamped management team - put in place after an end-of-season review between Rodgers and owners Fenway Sports Group following a disappointing season in which Liverpool faded to finish sixth.
Rodgers became the first Reds boss since the 1950s to fail to win a trophy in his first three seasons and, after a 6-1 thrashing at Stoke on the last day of the season, accepted his position was under threat.
Liverpool are also expected to appoint another new face to the coaching set-up before the start of the season as Lijnders is likely to be involved in elite player development and will continue to oversee some top academy players rather than acting as a direct replacement for Marsh.
Liverpool have named England Under-19s boss Sean O'Driscoll as their new assistant manager.