The 26-year-old - whose lack of form towards the end of the season with Arsenal led to his being omitted from the World Cup squad - signed a three year contract with the Hammers.
"It feels good, it feels special", said Wilshere told the club's official website.
"My family and a few of my friends are West Ham fans so everyone's buzzing".
Despite those concerns and a decent loan move in 2016/17 at Bournemouth has seemingly seen Wilshere regain his fitness back and last season he featured in 38 games for Arsenal across all competitions.
"The 34-cap England worldwide put pen-to-paper with the Hammers on Monday and will fly out to Switzerland to link up with Manuel Pellegrini's squad at their pre-season training camp in Bad Ragaz".
First boys freed from Thai cave after 2 weeks: updates
By the time he posted the test drive videos, four boys had already been rescued and the operation was suspended for the night. Former Thai Navy SEAL Samarn Kunan died trying to get oxygen to the group, which just how unsafe getting them out would be.
"I think it was a number of things", he said.
Manchester United have been the club predominantly linked with him, as they are with the vast majority of breathing humans, but West Ham's recruitment drive this summer looks set to finally claim him.
"Most importantly, he is hungry to play for West Ham, and determined to reproduce the level of performance that he has shown in the past".
It was confirmed last month that Wilshere would be leaving Arsenal, having spent his entire career there to date, after discussions with new manager Unai Emery.
West Ham have also initiated contact with Borussia Dortmund over the possible signing of Andriy Yarmolenko and remain in talks with the German club.