Sprint, the No. 3 U.S. mobile service provider, already owns just over 50 percent of Clearwire's shares and had increased its offer to $3.40 per share last week under pressure from activist shareholders.
Dish, which is also locked in a battle with Japan's SoftBank to acquire Sprint, raised its bid just two days before the Sprint offer goes to a vote.
"The Clearwire spectrum portfolio has always been a key component to implementing our wireless plans of delivering a superior product and service offering to customers," Charlie Ergen, Dish chairman and co-founder of Dish, said in a statement.
Dish's offer values Clearwire at $6.47 billion, according to its shares outstanding as of May 29.