Grosjean, part of the France team who won the Davis Cup title in 2001, replaced Yannick Noah after the French federation's initial choice Amelie Mauresmo opted not to take up the role.
Former world number one Mauresmo, who would have become the first woman to captain the team, chose to work with French player Lucas Pouille.
"It's a great honour to be named captain of the French Davis Cup team because I've always been attached to this competition," Grosjean, who will also lead the men's delegation for the 2020 Olympics in Tokyo, said in a statement.
"This post, which now has an Olympic dimension, promises to be exciting."
France tennis chief Bernard Giudicelli said the team would be stronger than ever with Grosjean's appointment.
"Sebastien's enthusiasm is proof of this and I'm happy to see a former winner take on the role. His knowledge of professional tennis, in all its forms, will be a valuable asset for our federation."
Grosjean, a four-times Grand Slam semi-finalist and winner of four ATP titles, has coached compatriot Richard Gasquet and Australia's Nick Kyrgios since his retirement in 2010.
France were beaten by Croatia in last month's Davis Cup final in Lille.
As runners-up, they will not play in the February qualifying round of the tournament, which has been revamped.
The traditional World Group format will be replaced by an 18-nation finals week to be held in Madrid in November.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
Share
