McHugh joined ATK from Scottish Premiership side Motherwell on a two-year deal.
McHugh was part of the famous Bradford City squad that reached the finals of the 2013 League Cup, becoming the first fourth-tier club in England to achieve the feat in 51 years.
He has played for Ireland 14 times - seven times in the U-17 team, five times in the U-19 team and twice in their U-21 team. He is yet to represent them in the senior team.
He is primarily a centre-back but can also play as a left-back. In the 2015-16 season for Plymouth in League Two, the manager deployed him as a midfielder.
"Carl McHugh is a very versatile and exciting player. His talent and his leadership skills will impact the team in a very positive way. I welcome him to the ATK family. Michael Soosairaj and Michael Regin are experienced players who have been playing competitive football in India. Their understanding of the game, their attacking style will add value to ATK," head coach Antonio Habas said in a statement.
Soosairaj joined ATK from Jamshedpur FC where he scored four goals in 14 matches during the 2018-19 season. Soosairaj has been signed on a five-year contract. The third signing Regin also played as a midfielder for Chennai City in the I-League.
Soosairaj and Regin will be expected to form a midfield partnership with the experienced Manuel Lanzarote Bruno, who has been retained from last season.
( With inputs from IANS )