Tom Bradshaw will join the Lions on a loan deal to start with, and will be made a permanent addition in January for a fee of over £1million.
Bradshaw's fee will beat Millwall's current transfer record which stands at £800,000 for the signing of Paul Goddard from Derby.
According to 'Sky Sports' Bradshaw has already passed a medical and they are working out formalities for his move to the Den.
Bradshaw will become Harris' sixth signing of the window, and he will add to an already strong strikeforce of Lee Gregory, Steve Morison and Tom Elliot.
Millwall had attempted to bring in the striker earlier in the window, but they were unable to come to a deal with Barnsley.
Bradshaw scored 12 goals in 43 matches for Barnsley last season, as the side were relegated to Sky Bet League One.
He has made five appearances this season, and scored in the sides' 2-0 victory away to Bradford.