The 5ft 2in Mexican international will reinforce the team's midfield in the Clausura championship, the club said in a statement.
America, based in Mexico City, gave no further details of the deal for the 24-year-old Bermudez but added that Atlante goalkeeper Moises Munoz would also arrive at the club in a straight swap for Armando Navarrete.
They are the first signings made by former Atlante coach Miguel Herrera who was appointed 10 days ago to replace Alfredo Tena, sacked after America finished second from bottom and failed to make the eight-team knockout phase of the Apertura championship.
The Clausura is the second of two championships in the season.
America put their entire squad, including half a dozen South American internationals, on the transfer list after their last match in the Apertura, a 3-1 defeat at Cruz Azul three weeks ago.
The Mexican giants, founded 95 years ago, had their best years in the 1980s when they won five of their 10 league titles.
Two championships in the last nine years - the Clausura in 2002 and 2005 - are a meagre return for the millions of dollars pumped into the club by media giant Televisa.
