Napout, 57, was arrested in Zurich at the request of US authorities last week and is currently banned from football.
He was arrested at a hotel along with fellow Fifa vice-president Alfredo Hawit, 64, on suspicion of accepting millions of dollars of bribes.
Uruguay FA chief Wilmar Valdez will replace Napout as interim Conmebol president until January.
Napout and Hawit, the interim president for North, Central America and Caribbean football, were among 16 current and former senior football officials indicted on 4 December by US authorities investigating corruption in the organisation.
The US Department of Justice alleges the 16 were involved in "racketeering, wire fraud and money laundering conspiracies" that saw them solicit and receive "over $200m (£132m) in bribes and kickbacks".
The total number of individuals and entities - such as sports marketing companies - charged to date is now 41. Of those, 12 individuals and two sports marketing companies have already been convicted as a result of the ongoing investigation.
Napout was elected as Paraguayan Football Association president in August 2007 and served until 2014, when he took over the Conmebol presidency on an interim basis.
He was elected to the Conmebol presidency on a permanent basis in March and was expected to serve until 2019.
"With the resignation of Mr Juan Angel Napout as president, the congress was convened for the election of officers [president and vice-presidents] for 26 January 2016," a Conmebol statement read.
Colombian football federation chief Luis Bedoya and his Colombian counterpart Sergio Jadue resigned their positions as Conmebol vice-presidents after pleading guilty to racketeering conspiracy and wire fraud.
Fifa vice-president resigns from Conmebol
12 December 2015
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Fifa vice-president Juan Angel Napout has resigned as president of Conmebol, South America`s football confederation.
