The 35-year-old central defender played under the new Hawks manager at both Eastleigh and Sutton United.
Now he is looking forward to helping the Westleigh Park outfit in their mission to get promoted back to the National League.
Beckwith said: ‘Once I was told that my contract wasn’t being renewed at Sutton I spoke with Paul.
‘I was delighted to get it all done. I've been down this way before and know the Hawks fans are very passionate.
‘It is something I am looking forward to.
‘I have enjoyed a lot of success playing under Doswell in recent years.
‘In my first year we got promoted from Conference South and we have also had a couple of excellent cup runs.
‘In the cups we played against the likes of Wimbledon and Arsenal.
‘We had some great times and once I knew Dos was interested it was a no-brainer for me.
‘Although the season has just ended I am already keen to get started on the next one.
‘It is nice to have a couple of weeks rest after a long, tough National League season.
‘At the same time I am one of those players who after a couple of weeks is itching to get started again.’