The 29-year-old Henderson made 31 appearances for Stranraer last season after joining from Ayr United but was out of contract this summer.
It was his second spell with the Third Division club, having left to join Queen of the South in 2006.
Millar told Clyde's website: "Murray has great leadership qualities and a tremendous will to win.
"His experience will be of huge benefit in the coming season as we will, in the main, have a very young group of players, inexperienced at SFL level."
As well as signing Henderson and Cochrane, Millar has secured top scorer Willie Sawyers on a new contract.
Source: BBC Sport
Source: BBC Sport