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The former Town Trainee passed a medical last week and agreed terms with the club earlier this afternoon, signing a two-year contract in the process.
The 21-year-old, who can also play in midfield will join up with his new club when his registration officially passes to the club on July 1st.
"Scott played quite a number of games in the Championship when I was at Portman Road," boss Willie Donachie told the club's official site.
"He's desperately keen to prove himself here at Millwall and get back to that level here.
"You can't have too many good left footed players in your squad and I'm sure Scott will prove a real asset for us."