The former Weymouth midfielder has penned a two-year deal at Westleigh Park following four seasons with the Terras.
Doswell admitted he thought it was highly unlikely 'loyal' McCarthy would leave the Dorset club.
But he quickly made moves to try to bring the former AFC Bournemouth player to the club after learning he was seeking a new challenge.
Doswell says McCarthy, who featured 40 times and scored seven goals for Weymouth in the National League last term, was a 'specific target' - and he's delighted to have won the race to get his signature.
The Hawks boss said: 'When we were made aware he was available he was someone we were keen to speak to, and someone who would have been on our target list had we been aware he was available.
‘He’s been very loyal to Weymouth over the years and I suppose that’s why clubs like ourselves never thought we’d get the opportunity to speak to him.
‘We were made aware a few weeks ago that Jake would not be signing another contract with Weymouth and he was very keen to come down and be part of the project. He was a real specific target.
‘He was someone who we rated highly when he played against us last year, he was a big part of Weymouth getting up into the National League.
‘Again, it’s another leader, someone who’s captained Weymouth for two or three seasons.
‘He can score goals from midfield, especially from set-pieces, very good and under-rated in the air.'
Doswell made it clear McCarthy and the club's other six summer signings are all arriving with one goal - winning promotion in 2021/22.
For Hawks' latest addition, his move represents a drop down in level.
But Doswell says it's down to McCarthy and the squad to make sure they're playing fifth tier football again after next season.
He said: 'I suppose the one thing he will find difficult in some respect is leaving the club (Weymouth) and the supporters because he’s very close to them.
‘Sometimes in your career you move on; whilst he’s dropping down a level technically, his job is to get this club back to that level and that’s what he’s been tasked here to do.
‘We’re not messing about, we want to get up, it’s a two-year contract and part of that two years is to make sure we’re in the National League.’