Archer's return eases pressure on an England fast-bowling department that has been hit by a number of injuries.
Mark Wood, Gus Atkinson, Olly Stone, Josh Hull and the uncapped Sonny Baker have all been sidelined.
Archer joins Chris Woakes, Brydon Carse, Josh Tongue, Sam Cook and Jamie Overton as fast bowlers in the squad.
Woakes, Carse and Tongue played in the win at Headingley and England could be tempted to stick with the same XI at Edgbaston.
After the win in Leeds, former England captain Michael Vaughan told Test Match Special: "The good thing is that Jofra is back in the equation - but I'd like to see him play another four-day game.
"He's not played the longer format for four years so why, on the back of one game for Sussex against Durham, would you rush him back?
"We know the intensity at Test-match level is so different to county cricket. Let him play another four-day game - I would go with the same line-up, as long as the bowlers are fine and there are no niggles."
Sussex coach Paul Farbrace, also a former England assistant coach, told BBC Radio 5 Sports Extra: "He bowled with good pace, good accuracy and his body's in good shape which is fantastic
"We would all love to see Jofra playing for England because he makes England a much better team, and he would give them a much better chance of winning the big series.
"Let's look after him, let's be careful with him. All I will report back to them is that he bowled nicely, he looks like he's in good rhythm, he's bowled 18 overs and it's up to them whether they pick him."
One scenario could be for Archer to sit out the Edgbaston Test, spend the week around the England team, then be available for the third Test at Lord's the following week.
That is the ground where he made his Test debut in 2019, famously duelling with Australia's Steve Smith.