Welch, currently the Leicestershire bowling coach, will work with the side in the lead up to the fourth ODI at The Oval and then remain with them during the game, while Silverwood has been given permission by Essex to work with England during the third ODI in Bristol.
Wasim Khan, the Leicestershire chief executive, spoke to Paul Farbrace, the England assistant coach, on Tuesday afternoon and agreed to release Welch from his county obligations for a couple of days.
"This is a great opportunity for Graeme," Wasim told ESPNcricinfo. "He is proving an excellent coach and we wouldn't want to stand in his way."
Welch confirmed to ESPNcricinfo he was interested in the role, calling it "the pinnacle of my profession" and said he was not going to apply for the role of head coach at Leicestershire vacated by the departure of Pierre de Bruyn. After a troubled reign as head coach of Derbyshire, Welch has concluded he is better suited to the role of bowling coach.
The England bowling coach role became available when Ottis Gibson left to take up the position of head coach with South Africa.
Trevor Bayliss, the England head coach, has previously stated that the ODI series will be utilised to look at some of the options for the bowling coach role.
Andy Pick, the Nottinghamshire bowling coach, will be with the side for the T20I at Chester-le-Street and in the build-up to the match.