The former 'Suits' actress' dress was reported to have cost as much as $107,000 and her opulent choice attracted lots of criticism.
But Alexi insisted he found the couple - who are set to marry at St George's Chapel at Windsor Castle on May 19 - to be extremely easy to deal with, saying they were "so naturally in love".
He told Entertainment Tonight: "She was actually a godsend because obviously Prince Harry has done many photos before, but she really knew what goes into a photo shoot because she's done it so many times before.
"So, it was wonderful to have her as a sort of coach on set. He kind of led her through and she led him through, and she just made it very nice and easy."
Alexi joked that he only got the coveted assignment because "nobody was available and they scraped the bottom of the barrel".
But he subsequently admitted he was chosen by Meghan, 36, following a recommendation from one her friends.
Alexi recalled: "When I went to meet them to see if we vibed, they were just cutesy and every time they looked at each other they were like, [giggling].
"I was like, 'This is gonna be great. This is gonna be easy.' I said, 'I just want to shoot you like this. This is what you're like.'"