Willis made a name for himself at Wimbledon last year when, ranked 772nd in the world, he battled through pre-qualifying, qualifying and the first round of the main draw before securing a meeting with Roger Federer.
The 26-year-old from Slough lost that game in straight sets but was unable to qualify for the singles draw this year, losing his final qualifier.
Willis, along with 18-year-old Clarke, will take on the pairing of Austrian Oliver Marach and Croatian Mate Pavic in the third round.
(This story corrects seeding of Herbert and Mahut to second in first paragraph.)
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(Reporting by Simon Evans; Editing by Robin Pomeroy)
