Bolton boss Gary Megson had been after the Toulouse front man since the start of the year and is rumoured to have paid a club record £10 million ($19.9 million), beating the previous mark in purchasing French striker Nicolas Anelka from Fenerbahce.
Megson had been tracking Elmander as a replacement for Anelka after the Frenchman was sold to Chelsea in the January transfer window.
Elmander joined Toulouse in 2006 in a move from Danish Brondby. He played 59 games for the French club, scoring 22 goals.
Elmander was a regular starter for the Sweden team in the qualifying campaign for Euro 2008 but lost his place to the returning Henrik Larsson alongside Zlatan Ibrahimovic in the Swedish attack. He started two games on the right-side of midfield as a replacement for the injured Christian Wilhelmsson.