Argentina's inclusion in the southern hemisphere Rugby Championship, which finishes in October, and the Pumas' three November internationals means Agulla will not be available to Bath full-time until December.
But Bath coach Gary Gold is confident the experience of playing regularly against the world's top three nations will only make Agulla a better player, and therefore benefit the club.
"We're really excited to have Horacio join Bath Rugby for the new season," Gold said.
"He's a very good player who is able to play two positions at a high level which brings great diversity and strength in depth to the team.
"We believe his exposure playing for Argentina in the new Rugby Championship format against the All Blacks, South Africa and Australia will further develop him as a player and Bath Rugby can only benefit from that."
Agulla's move from Leicester, for whom he made 48 appearances, will be finalised upon confirmation he has been granted a work permit.
The 27-year-old was voted Leicester fans' player of last season, when the Tigers finished as Premiership runners-up to Harlequins.
"I'm really excited to be joining Bath Rugby and hopefully helping them to challenge for silverware next season.
Bath play a good brand of rugby that I believe will suit my game and I'm excited to work with the new coaching team," Agulla said.
"They have some excellent players in their squad and my first challenge is to get into the side and make that starting shirt my own."
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