“It’s obviously an honour and a fantastic privilege,” Enqvist said in a statement released by the federation.
Enqvist, 35, retired from the game in 2006 with 19 ATP Tour titles and an appearance in the final of the 1999 Australian Open to his name.
He twice won the Davis Cup with Sweden, in 1997 and 1998, having tasted defeat in the 1996 final against France.
In total he played 26 matches for his country between 1995 and 2004.
“I hope that my experiences as a player will serve me well and I intend to create a link between the team and young players from the junior team.”
Enqvist’s predecessor Wilander, a former world number one, announced on Tuesday that he was stepping down from the role he has occupied since 2003 in order to spend more time with his family.