The 31-year-old has 10 caps for his country, the last having been earned in a friendly against Germany in November 2011, but endured a torrid 2013-14 campaign.
Braafheid did not make a single appearance for Hoffenheim and was made to train with the club's under-23 squad.
The defender enjoyed previous spells at Bayern Munich and Celtic, before joining Hoffenheim in 2011.
Braafheid then made 31 Bundesliga appearances at Hoffenheim, before being loaned to Dutch side Twente for the 2012-13 campaign.
That transfer marked a return to the club he left for Bayern in 2009, and Braafheid made 25 league starts before returning to his parent club, where he failed to make an impression.
Friday's announcement offers Braafheid the chance to prove his worth once more, with Lazio looking to mount a challenge to return to European football after finishing ninth in Serie A last season.