Giedrius started his professional career with FC Siauliai in 2005, making 40 league appearances in a two-year spell.
In January 2008 he joined Romania Liga 1 side Unirea Urziceni and featured in the Champions League group stages before joining Russian Premier League side Rubin Kazan in 2010.
He spent three seasons with the club before returning to Romania with Steaua Bucharest in June 2014, and his displays that year earned him the Lithuanian Footballer of the Year award.
A successful season secured a move to Premier League Watford, where he made his top-flight debut in a 3-2 win against Aston Villa.
In January 2016 he joined Espanyol on loan, making his La Liga debut against Real Madrid, before returning to Vicarage Road at the end of the season.
In August 2017 he joined Romanian side CFR Cluj and won league titles in his first two seasons, likewise the Romania Super Cup in 2018. He was also named in the Liga 1 Team of the Season.
Giedrius made his debut for Lithuania against Moldova in November 2008 and has since made over 20 appearances for his country.