Infantino, a 45-year-old Swiss-Italian, is currently general secretary of European body UEFA and claims to have overwhelming backing from his own continent, making him one of the front-runners in next month's FIFA vote.
The election was called after the organisation was plunged into the worst crisis in its 111-year history last May, with the arrest of officials by American and Swiss authorities probing corruption allegations.
"The CONMEBOL executive committee has decided to back Gianni Infantino's candidacy and plan of action for the presidency of FIFA," the confederation said in statement. It said the committee "expressed its unanimous approval to vote as a block for Gianni Infantino".
Infantino is one of five men bidding to replace Sepp Blatter at the helm of FIFA, whose 209 member associations each have one vote in the February 26 electoral congress.
Blatter, who had been in charge at FIFA since 1998, was banned from football for eight years in December.
News of 10 secured votes from South America is a further boost to Infantino's bid after he collected seven promised votes from Central America's UNCAF organisation on Monday.
CONMEBOL had previously backed Infantino in November, before several of its officials featured in the second Department of Justice corruption indictments.
The December 5 indictments saw charges against then CONMEBOL president Juan Angel Napout of Paraguay as well as general secretary Jose Luis Meiszner of Argentina, along with officials from Brazil, Peru, Ecuador and Bolivia.
The strongest challenger to Infantino appears to be Asian Football Confederation (AFC) president Sheikh Salman Bin Ebrahim Al Khalifa of Bahrain.
Former FIFA deputy general secretary Jerome Champagne of France, South African businessman and politician Tokyo Sexwale and Jordan's Prince Ali Bin Al Hussein are the other candidates.
Forty-one individuals, many of them national association presidents, and entities have been indicted in the United States for bribery, money laundering and wire fraud since May in the organisation's worst-ever corruption crisis.
Blatter and Frenchman Michel Platini, who had been a strong favourite to succeed him, were banned over a payment of two million Swiss francs ($2 million) made to the Frenchman by FIFA with Blatter's approval in 2011 for work done a decade earlier.