The American, three times a runner-up at the grand slam tournament, visited the grasscourt club on Friday for "a spot of tea" with Henman while in London competing at the Statoil Masters event at the Royal Albert Hall.
"I was able to take him to Wimbledon a couple of days ago because he's being made an honorary member, which he was so excited about, having been a three-time finalist," Henmanm said in an interview with the Tennis Podcast.
Honourary membership of the elite club usually requires a Wimbledon title, but Henman said former world number one Roddick, who quit in 2012 aged 30 deserved the accolade.
"If you win the tournament you become a member automatically but I think with his impact in that event and his rapport with the British crowd it was felt that it would be a really nice gesture," Henman added.
"He was given a few gifts, one of them being a club tie, which is completely useless because he doesn't know how to tie a tie!"
Roddick, runner-up in 2004, 2005 and 2009, is making his first appearance on the seniors tour this week and on Saturday reached the final when he beat 2002 Wimbledon semi-finalist Xavier Malisse 6-4 6-2.
He will play fellow debutant Fernando Gonzalez at the Royal Albert Hall after he overcame Henman 6-4 2-6 10-6.
(Reporting by Martyn Herman; Editing by Ian Ransom)
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