Walcott shared one image of his flexibility being tested during his medical and another of him being checked out by a member of Everton's staff.
Sky Sports News understands the fee for the forward is in the region of £20m, with the England global set to take the No 11 shirt vacated by Kevin Mirallas who has re-joined Olympiakos on loan.
Many may have suggested that the move north for Walcott is a possible attempt at improving his chances to be named in Gareth Southgate's England squad for the World Cup.
And the 28-year-old told a news conference on Thursday there was no great fanfare when he came to leave Arsenal's training ground.
Everton continues to supply its managers with top-end talent, adding Theo Walcott to its expensive season of boys which includes Gylfi Sigurdsson, Wayne Rooney, Cenk Tosun, Jordan Pickford, and Michael Keane.
He also had a decent record last season, scoring 19 goals in 37 games, the second-best season of his career in terms of goals scored. "Alan (Pardew) picked his first win up last week and I just hope we're not feeling the nerves again because we've not won for three matches".
"There's something about this move I've just felt good about", he said. I'm sure he had other decisions to make but felt this was the right place.
Walcott gives Allardyce another option out wide alongside Yannick Bolasie, Ademola Lookman, Aaron Lennon and Nikola Vlasic and brings with him a huge amount of experience. Everton have had a habit in recent years of finding ways to pull at least some degree of lost potential out of players, and they very much need a winger with the kind of skill that Walcott once displayed on a regular basis. The manager (Sam Allardyce) is very ambitious and I feel like the club is going in the right direction.
Although Walcott has a long affinity with Arsenal, the move felt like a necessary one for the England global.
"We do also play them soon as well, which I'm looking forward to".
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