Prior to that trip, England will play the Republic of Ireland, also at Wembley, for the first time since their infamous fixture in 1995 was abandoned after a riot by England fans at Dublin's Lansdowne Road.
Brazil are always a big draw card and the 6 February clash is given added relevance by the fact the South Americans, beaten finalists in the recent men's Olympic Final in London, are staging the 2014 FIFA World Cup.
Meanwhile officials will hope for a big crowd for what will be the Republic's first match at Wembley since 1991, with travelling fans only having to make a relatively short journey and a large expatriate community already in London.
News of these fixtures come after the FA announced their 150th anniversary would also feature a match in August between England and Scotland -- international football's oldest clash.
"2013 is a landmark year for The FA and an exciting England fixture programme in addition to Wembley hosting the UEFA Champions League Final will form a key part of the celebrations.
"As the most successful footballing nation, with great players and supporters, it will be fantastic to launch this important year in English football's history against such outstanding opponents as Brazil.
"We also look forward to hosting Republic of Ireland and Scotland at Wembley next year. These matches are sure to evoke great passion among supporters."
Meanwhile Bevington added the matches in South America would form a part of England's plans for the 2014 FIFA World Cup, a tournament for which they have still to qualify.
"We have been planning the fixtures in Brazil for over a year, as a key part of our preparation for 2014, subject to qualification," he said.
"Our players do not have any experience of playing in South America and it will undoubtedly be beneficial for the team to travel and play in Brazil, a year ahead of the World Cup. We negotiated our qualifying schedule with a specific view to allowing this.