Oastler, 30, has completed a move to Westleigh Park on a two-year deal after his contract at Oxford City expired.
Doswell revealed his delight at finally landing the defender he has been hoping to recruit since last season.
The Hawks boss cited the former Pompey youth player's experience and leadership qualities as a key attribute he'll bring to his squad in the push to reach the National League in 2021/22.
Oastler, based in Milton and head of coaching for the Westleigh Park-based Havant & Waterlooville Pro:Direct Academy, was captain for a large part of his four seasons at Oxford City.
And Doswell believes his second summer signing, along with others who will be joining the club, will bring key leadership qualities.
The boss said: 'He’s someone who we’d have liked to have got in a year ago. He was committed to Oxford City at the time, rightly so, but obviously I’ve watched him closely over this year with our academy players and I’ve been impressed with him as a person.
We’re signing him as a leader who knows this level but also the leagues above.
‘You need two or three in the group (leaders). We lacked a real leader last year in the dressing room.
'We were too passive at times so it was quite important that we do bring in two or three and that’s what’s going to be coming to the football club - Joe’s arrival is the first of those I would say.'
It represents a move closer to home for the defender, who came through the system at Pompey.
And Doswell sees Oastler becoming a mainstay at Hawks for many years to come.
He said: 'He genuinely wants to play for this football club, he’s a local lad, he’ll probably tell you himself he’d have loved Havant to come in for him earlier in his career - it didn’t happen for him for whatever reason.
‘He’s here now, he’s a young 30, he’s got the experience, he’s fit and I see him being a mainstay at this football club.'