Songaila started his basketball career with Lietuvos rytas Marijampolė in second-tier Lithuanian league, the LKAL in 1995.

Songaila was selected with the 50th pick of the 2002 NBA draft by the Boston Celtics, who eventually dealt his rights to the Sacramento Kings.

At the end of the 2008–09 season, Songaila became a starter because of the injuries suffered by teammates Brendan Haywood and Andray Blatche.

On June 23, 2009, he was traded to the Minnesota Timberwolves along with Oleksiy Pecherov, Etan Thomas, and a first-round draft pick for Randy Foye and Mike Miller.

[5] On September 9, 2009, he was traded to the New Orleans Hornets along with Bobby Brown in exchange for Antonio Daniels and a 2014 second round pick.

[6] On September 23, 2010, he was traded to the Philadelphia 76ers along with rookie forward Craig Brackins in exchange for Willie Green and Jason Smith.

[13][14][15] In August 2018, he became a quality assurance assistant in the video department for the San Antonio Spurs of the National Basketball Association (NBA).

[18] On November 1, 2024, he signed with Manisa Basket of Basketbol Süper Ligi (BSL), as an assistant coach to Kazys Maksvytis.