Flower relinquished his day-to-day responsibilities with the one-day and Twenty20 teams before Christmas, with Ashley Giles taking the reins, and Gooch has quickly followed suit.
From now on Gooch will devote himself to the five-day game, with Graham Thorpe taking over as batting coach for the forthcoming one-day tour of New Zealand.
Like Gooch, Thorpe is one of a distinguished group to play in 100 Test matches for England. He has been coaching the England performance programme and the England Lions since October 2010 and will now get the chance to work with the senior national side.
Like Giles, who last played for England six years ago, Thorpe is a player many of the current side will have grown up watching and scored 6,744 Test runs at 44.66 between 1993 and 2005.
Hugh Morris, the ECB's managing director of cricket, said: "Graham Gooch is going to focus now on Test cricket and on preparing batsmen for Test matches.
"We would like to focus on that area of the game. We've got back to back Ashes series coming up and a five-Test series against India in 2014. That's an enormous amount of very high-profile Test cricket and Graham will be focusing his attention on working one on one with our Test players.
"Graham Thorpe, who has been working with the performances programme and the Lions will be going as the one-day coach to New Zealand. (Thorpe's role) is for this tour initially and then we'll assess the situation at the end of that.
"We're very fortunate to have two (batting coaches) who've played 100 Test matches for England. Graham Thorpe is a very experienced one-day cricketer and Graham will have worked with a lot of the players who are going to New Zealand.
"He's made a really good impression as a batting coach and he's really looking forward to it."