Tom Simpson, the chart-topping band's keyboard player, was alleged to have been found in possession of cocaine in Glasgow's Sauchiehall Street on June 24th, 2006.
The 35-year-old had been scheduled to appear at Glasgow Sheriff Court next Tuesday.
However, a spokeswoman for the Crown Office has today confirmed that the case will not go ahead.
"Following further information received from Strathclyde Police, the procurator fiscal has taken the decision that no further proceedings are appropriate," she commented.
Simpson had been arrested a year after the alleged incident, following Snow Patrol's performance at the Live Earth climate change concert at Wembley Stadium on July 7th.
The keyboard player was released so as to appear at the band's headline show at the T In The Park festival the following day.
Charges against Simpson and the other man involved, Colin Kennedy, 35, have been dropped.
Snow Patrol - who had a number one album in 2006 with Eyes Open - also appeared at this year's V Festival in Essex and Staffordshire.