Andrésson, 19, joins on a month`s loan deal having been coached by Torquay`s assistant head coach Martin Kuhl at the Reading academy.
He also played under Torquay head coach Gary Owers in a loan spell at National League South outfit Bath City last season.
He signed for Reading from Icelandic team Afturelding and joins former Royals defender and fellow Icelander, Ívar Ingimarsson, in playing for United.
Ingimarsson made four appearances for the club on loan from ÍBV in 1999, scoring one goal.