The 31-year-old, who has been a regular opponent of the Pilgrims over the years in Guiseley, Bradford Park Avenue and Harrogate Town colours, will be lining up in amber and black for the 2019-2020 campaign, subject to final approval from the Football Association and National League.
Ainge, traditionally a centre-half, was converted into a centre forward by Harrogate boss Simon Weaver at one stage, but has now reverted to his more accustomed defensive role.
"Aingey has vast experience in this league and is very much the aerial and physical presence in both boxes that we lacked last season," commented United boss Craig Elliott to bufc.co.uk.
"He has shown a lot of determination and hunger to make this deal happen and I am very much looking forward to working with him."
Ainge will be United's ninth new recruit of the closed season.