The 26-year-old, who has scored 11 goals in 84 appearances during two years with the Iron, has signed a three-year deal with Pompey.
Barcham told the club's official website: "It wasn't really a big decision to make what with the size of the club and stadium and the terrific fanbase.
"After standing in the South Stand and gazing down on to the pitch, it looks a wonderful place for a winger to come and play.
"I like to go forward, attack and get at opposition players - this is the perfect place to be able to do that."
Blues boss Guy Whittingham added: "We didn't really have any out-and-out wide players in the team last season and I think it was important we got at least one in.
"Andy can give us a bit of excitement on the wing and offers us that touch of creativity that could prove to be the difference."