Graham, who turned 50 on Monday, has extensive managerial experience in the EFL with the likes of Bristol Rovers, Mansfield Town and Newport County – as well as a developmental role at Sheffield United.
Following a thorough three-week recruitment process, the Pilgrims have opted for the Irishman to become the club's new manager as they seek to retain the National League status earned in May.
He assumes immediate control of first team affairs at the Jakemans Community Stadium, as preparations continue for the visit of Braintree Town on Saturday.
Coughlan served Southend United for a number of years in assistant manager and first team coaching roles, before being appointed Bristol Rovers' permanent manager in January 2019, following a successful spell in caretaker charge.
A spell with Mansfield followed, following an approach from the Field Mill club, before a return to first team management unfolded at Newport in October 2022, after a stint at Bramall Lane coaching the club's under-23s.
At Newport, he preserved the club's EFL status in his first campaign at the helm, before taking the Exiles to the fourth round of the Emirates FA Cup in the following season where they exited the competition to Manchester United at Rodney Parade.
As a player, the Dubliner played over 500 games, including headline spells with the likes of Livingston, Plymouth Argyle and Sheffield Wednesday and earned three promotions.