Harlequins wing Visser and Gloucester centre Scott have each earned recalls and are in contention to represent their country for the first time since June 2017, while Nel's inclusion comes after the Edinburgh prop proved his fitness after a spell on the sidelines with a broken arm.
Head coach Gregor Townsend has also called up Tim Swinson, who has recovered from a hand injury, Josh Strauss and uncapped Glasgow Warriors hooker James Malcolm.
Duncan Taylor (head) and Richie Gray (calf) are unavailable, while Magnus Bradbury, Nathan Fowles, Murray McCallum and D'Arcy Rae have been left out.
BREAKING | Scotland add six to NatWest 6 Nations squad ahead of this Saturday’s Round 3 Test against England at BT Murrayfield (kick-off 4.45pm) - live on BBC #AsOne
— Scottish Rugby (@Scotlandteam) February 18, 2018
Scotland, who were thumped by Wales in their opening match but bounced back with a home victory over France, face England at Murrayfield next Saturday.
Eddie Jones' side will be looking to remain on course for a third successive Six Nations title and a second Grand Slam in three years.
Forwards: John Barclay (captain), Simon Berghan, Jamie Bhatti, David Denton, Cornell du Preez, Grant Gilchrist, Jonny Gray, Luke Hamilton, Rob Harley, Scott Lawson, James Malcolm, Stuart McInally, WP Nel, Gordon Reid, Josh Strauss, Tim Swinson, Ben Toolis, Hamish Watson, Jon Welsh, Ryan Wilson.
Backs: Mark Bennett, Nick Grigg, Chris Harris, Stuart Hogg, Pete Horne, Ruaridh Jackson, Huw Jones, Blair Kinghorn, Greig Laidlaw, Sean Maitland, Ali Price, Henry Pyrgos, Finn Russell, Tommy Seymour, Matt Scott, Tim Visser.
Photo Getty Images. Caption: Tim Visser celebrates a try for Harlequins