Midfielder McGugan is Carlos Cavalhal’s fifth signing of the summer and arrives at Hillsborough on a three-year contract.
The 26-year-old enjoyed two separate successful loan periods at The Owls last season, making 22 appearances and scoring three goals in the process.
McGugan also picked up two of Wednesday’s Player of the Month awards during a successful season in Yorkshire.
The midfielder began his career at Nottingham Forest and made 202 appearances for them before moving to Watford on a free transfer in 2013.
McGugan featured regularly in his first season at Vicarage Road but was deemed surplus to requirements in Watford’s last campaign before being loaned out to Wednesday.
The former England U19 international had previously said he was open to possibility of extending his loan deal to a permanent switch.
“If Sheffield Wednesday and Watford can do a deal, then brilliant, but it’s up to the clubs. I can only concentrate on playing well on the pitch,” he said earlier in the year.