Solís made his debut for Costa Rica in a September 1993 friendly match against Saudi Arabia and earned a total of 110 caps, scoring 6 goals. He represented his country in 30 FIFA World Cup qualification matches and played at both the 2002 and 2006 FIFA World Cups. He also played at the 1995, 1999 and 2001 UNCAF Nations Cups as well as at the 2002 and 2003 CONCACAF Gold Cups. He also played at the 1997 and 2001 Copa América.