"She is going to be the next president of Costa Rica," Solis told his supporters, while Guevara offered congratulations to "our president, Laura Chinchilla".
Addressing her supporters at a hotel in the capital, San Jose, Chinchilla said: "Thank you, Costa Rica. It's certainly a moment of happiness, but above all of humility ... I won't betray that confidence."
Chinchilla, who served as vice-president under Oscar Arias, the current president and Nobel-prize winner, has pledges to continue Arias's moderate free-market policies.
Under Arias's National Liberation Party (PLN) Costa Rica has been brought into the Central American Free Trade Agreement with the United States and initiated trade relations with China after a 63-year association with Taiwan.
But Critics of the government argue that Arias' administration catered to big developers to boost the economy at the cost of the nation's fragile ecosystems.
Costa Rica enjoys the highest standard of living in Central America and is renowned for not having an army and its role in ending the Cold War-era civil wars that wracked its neighbours.
The country is also Central America's oldest democracy with a record of 60 years of democratic elections.
Besides Guevara and Solis, six other candidates were also running in a race that tested the popularity of the PLN party, which has dominated politics in Costa Rica for the past six decades.
While Chinchilla will be Costa Rica's first female president, she will be Latin America's fifth.