Joseph, a regular for England for two years, was left out of the squad that beat Italy two weeks ago as coach Eddie Jones experimented with his midfield, but reclaims the number 13 shirt from Ben Te'o, who drops to the bench.
In two other changes announced by Jones on Thursday, Jack Nowell, who scored two late tries off the bench against Italy, will start on the right wing and Ben Youngs returns at scrumhalf for Danny Care.
Winger Anthony Watson, also back from a succession of injuries, is on the bench and set to play his first test since June, leaving no place in the squad for Jonny May.
The starting pack is unchanged but Vunipola comes into the replacements after his quicker-than-expected recovery from a knee injury.
The number eight has played one club match since suffering ligament damage in November that was initially thought to have ruled him out of the whole tournament.
Defending champions England top the Six Nations standings after three victories and another on Saturday would take their winning run to 18 matches, level with New Zealand's tier one world record.
Should Wales beat Ireland in Cardiff on Friday then England can secure the Six Nations title with a game to spare by beating the Scots.
However, they will need to show a marked improvement from their last outing against Italy, where they struggled for more than an hour before a strong finish earned their 36-15 victory.
"We want to give our fans a really good performance," Jones said in a statement. "We've worked hard in this Six Nations and feel like a good performance is just around the corner.
"This is the 124th Calcutta Cup and I feel humbled and honoured to be part of such an historic rugby occasion. "It's the oldest international fixture and means a lot to both countries. We treasure the experience."
Scotland have had precious little to treasure from the fixture in the recent past, failing to win at Twickenham for 34 years.
However, they will arrive in good heart this time having won two games and delivered some exciting performances, and would love nothing more than to be the team that brings England's winning run to an end one short of the record.
Unfortunately for the visitors, their scrum has really struggled, even in their victories, and with England's pack looking strong and settled, the odds remain very much in favour of another home win.
England team to play Scotland (1600 GMT):
15-Mike Brown, 14-Jack Nowell, 13-Jonathan Joseph, 12-Owen Farrell, 11-Elliot Daly, 10-George Ford, 9-Ben Youngs; 8-Nathan Hughes, 7-James Haskell, 6-Maro Itoje, 5-Courtney Lawes, 4-Joe Launchbury, 3-Dan Cole, 2-Dylan Hartley (captain), 1-Joe Marler.
Replacements: 16-Jamie George, 17-Mako Vunipola, 18-Kyle Sinckler 19-Tom Wood, 20-Billy Vunipola, 21-Danny Care, 22-Ben Te'o, 23-Anthony Watson.
(Reporting by Mitch Phillips; Editing by John O'Brien)
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