The ambitious move for the 33-year-old comes as United prepare for their first season as a senior club in the Scottish football pyramid system.
Nicoll joined Clyde for a second spell in 2017 - he previously spent a season there in 2012-13 - and was later appointed club captain.
He was part of the Bully Wee squad who ended the club's near-decade exile in Scottish football's bottom tier last year by winning promotion.
However he was released by the club last summer and spent last season with Stirling Albion.
Nicoll has also had spells with Albion Rovers, Stranraer, Dumbarton, Arbroath and Annan Athletic and his experience will be key for United, under new boss Kieran McAnespie, as they take their place in the new West of Scotland League.