Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The 27-year-old has been a free agent since he left MLS side Portland Timbers towards the end of last year.
The defender, who left Ibrox in 2010 after breaking through as a youngster, has signed a two-year deal.
However, Smith will only be able to feature as a trialist before September 1. Rangers are banned from registering players until after the closure of the summer transfer window following the deal that was struck with the Scottish Football Association last summer that allowed them to reform as a newco after the old Rangers were liquidated.
But the player will join up with his new team-mates for pre-season training and could play in as many as three Irn-Bru Second Division fixtures as a trialist.
Smith has already met up with many of the current Light Blues squad after Rangers boss Ally McCoist granted him use of the Murray Park training facilities following his return from the US.
The Scotland B international joins goalkeeper Cammy Bell, midfielders Nicky Law and Arnola Peralta and forwards Jon Daly and Nicky Clark in agreeing moves to the Glasgow giants this summer.
He came through the youth ranks at the Third Division champions and made his professional debut back in November 2004 in a 3-2 win over Hearts.
He went on to make 64 competitive starts for the club in total but had his progress curtailed by a long-standing pelvic problem.
Bellshill-born defender Smith eventually moved on to Norwich City in 2010 before turning out for Aberdeen and Preston North End.
The move has already been welcomed by Rangers forward David Templeton, who posted on his official Twitter site: "Glad to see @Steven26Smith has signed today! Top lad and very good footballer."