Byram officially made the switch from Championship outfit Leeds United to Upton Park on Wednesday, and Sullivan wasted no time heaping praise on his club's newest acquisition.
"He has been bought for the future and long term he could well be an English international," Sullivan told West Ham's official website.
"He is a utility player who can play anywhere down the right hand side and when played in a forward position he can score goals. He has already scored three times for Leeds this season.
"He is still young and is improving all the time. His uncle and cousins are West Ham United season ticket holders.
"We had planned to sign him in the Summer, but we were forced to move sooner as it was clear that Everton had agreed terms with Leeds to sign him."