Draper will have to fight his way back up the rankings, having fallen out of the top 100 during his lay-off.
He is in the main draw for Wimbledon, which begins a week after Eastbourne on Monday, 29 June, but will be hoping to get plenty of match practice on the grass courts this week.
“I don’t know how these competitions [Eastbourne and Wimbledon] are going to go in terms of my wins and losses,” Draper said.
“I want this period to be past me now, of dipping in and out of the tour and coming back for one or two weeks.
“I feel like I’m able to be the player I want to be again on the court, which is a really great thing after a year of struggle.”
Draper will be accompanied in Eastbourne by three-time Grand Slam champion and former world number one Andy Murray.
Murray has joined up with Draper for the grass-court season but told BBC Sport he he hopes to work with him on a long-term basis.
Two-time Wimbledon winner Murray is set to be courtside to watch Draper take on fifth seed Nakashima at Devonshire Park.
“I’ve lost a lot of confidence in my body over the last year and having someone who believes in you is a big positive,” Draper added.
“Our relationship is very special, and that gives me a bit more energy, especially in a moment where I’m coming back and need to have that good energy around me.”
