In the most expensive day in the club's history, Sunderland concluded their lengthy pursuit of Fletcher at lunch before also adding the signature of Johnson in the evening for a combined outlay believed to be in the region of £25 million.
Johnson - who has won 12 caps for England, scoring twice - leaves City after failing to secure a first-team place under Roberto Mancini and the 25-year-old has signed a four-year deal to return to the north east, where he previously represented Middlesbrough.
Manager Martin O'Neill said: “Adding quality players to the squad has been our main aim this summer and Adam certainly fits that bill.
“He has terrific ability, great delivery and I'm sure he is a player who will excite our fans.
“I couldn't be more delighted to have him at the football club.”
Fletcher, 25, has also signed a four-year contract at the Stadium of Light and, unlike Johnson, will be available for the Black Cats' Premier League game against Reading on Saturday.
The Scot caught the attention after scoring 12 goals in each of the last two top-flight campaigns for Wolves and is reported to have cost in the region of £14 million.
O'Neill said: "It has been no secret that we needed to strengthen our attacking options and Steven has a proven track record of scoring goals."