The 50-year-old - who has won two league titles as manager - moves to the Jakemans Community Stadium from National League North rivals the Poppies, who he has guided to eighth in the table, a point behind the Pilgrims with a game in hand.
Cox has previously managed Mansfield Town, Eastwood Town, Torquay United, Barrow and Guiseley as well as Kettering.
Cox won the 2012-13 Conference Premier with the Stags and the 2008-09 Northern Premier League title with the Badgers.
His number two at Mansfield was former United boss Adam Murray.
Midfielder Paul Green has been taking charge of the Pilgrims since Craig Elliott left earlier this month after more than four years in the Boston dug-out.
Green will take charge of tomorrow's visit to Spennymoor, with Cox watching from the stands.