Morris has previously managed Goole AFC, Frickley Athletic and most recently Worsbrough Bridge Athletic.
The former striker was released from Rotherham United as a teenager and went on to play for Worksop Town, Hallam, Belper, Frickley, Harrogate, Droylsden, Hucknall, Stalybridge, Buxton and Matlock.
Mike Carmody resigned as Armthorpe boss last month with the team struggling near the foot of NCEL Division One.
Managerless Welfare subsequently won two of their next three games prior to lockdown to move up to 13th in the table.
Morris said: “I am very pleased to be joining a great club like Armthorpe Welfare who are a side I’ve had great battles with during my time as both a player and a manager.
"I believe the pitch is up there with one of the best in the league and with the bar improvements things are going in the right direction.
“I can’t wait to meet the lads when this lockdown has ended. I’m very lucky to be inheriting a fantastic squad, many I know and many I’m looking forward to getting to know.
"I hope to carry the confidence on from the last two wins in which Steve, Alan, Adam and Reece did a fantastic job to help the team move forwards.”
Welfare chairman Steve Baskerville said: “I am delighted that we have been able to appoint a manager of the calibre of Lee Morris. He possesses all the attributes that we were looking for in a manager.
"There were some very strong applications and the committee had a tough decision to make but we are sure that Lee will prove that we have made the right call once we can get back to playing football again.”