Bassett has been a long-time mentor to Wise and it is understood they have been in regular contact throughout the past few months.
The duo first linked up in 1985 when Bassett, then manager of Wimbledon, signed Wise as a teenager from Southampton on a free transfer and they have gone on to work together at four different clubs.
Wise said last night: "I am delighted that 'Harry' has agreed to join Leeds United. He brings with him a wealth of experience, having been there, seen it and done it. We know each other well, having worked together before, and I'm looking forward to working with him again.
"We have had a good start to the season and Harry is keen to play his part in helping us move further forward, based on the foundations we have already laid."
Bassett's last job was at Southampton when he took temporary charge of the Saints following Harry Redknapp's departure to Portsmouth late in 2005.
George Burley's subsequent appointment then saw the former Sheffield United manager leave St Mary's along with Wise, who had stepped in as assistant.
The pair had previously worked together at Leicester City and Millwall when, like now, Wise was in charge and his mentor on the coaching staff.