Richardson, 20, joined the Owls in December and was part of their surge up the league table, as they narrowly missed out on the play-offs.
He has agreed a deal to stay at the club until the end of the 2020/21 season.
Joining him in the squad is defender Fixter, who arrives from Spalding United.
The centre-back has impressed the club’s management during pre-season.
Keep up-to-date with our exclusive email newsletters.
Subscribe