Nole will play at the ATP 250 event in preparation for the only tennis Grand Slam on grass, The Championships, Wimbledon.
Novak will be making his debut appearance at the ATP World Tour 250 grass-court tournament at Devonshire Park.
The Austrian sixth seed beat the defending champion in straight sets 7-6 (5), 6-3, 6-0 in two hours and 15 minutes.
Novak continued his good run on Parisian clay as he defeated Albert Ramos-Vinolas 7-6 (5), 6-1, 6-3 to reach the last 8.
The second seed moved into the French Open R4 for the 11th time with a five-set win over Diego Schwartzman.
Novak cruised into the French Open third round with straight sets win over Joao Sousa (6-1, 6-4, 6-3).
The reigning title holder started his Roland Garros campaign with a 6-3, 6-4, 6-2 win over Marcel Granollers.
Novak won his first French Open title in 2016 and completed career Grand Slam beating Andy Murray in the final (3-6, 6-1, 6-2, 6-4).
The world no.2 and four-time champion lost the Italian Open final to no.16 seed Alexander Zverev 4-6, 3-6.
Djokovic produced his best tennis to beat no.8 seed Dominic Thiem 6-1, 6-0 in just 59 minutes on Saturday evening.