The eurozone's fourth-largest economy expanded by 0.4 percent on a quarterly basis, the Bank of Spain said in a monthly report, citing initial data.
It was the sharpest quarterly growth rate since the first quarter of 2008 when a decade-long property bubble imploded, tipping the nation into a double-dip recession that wiped out millions of jobs and flooded the nation in debt.
"In the first quarter of 2014, the Spanish economy continued on a path of gradual recovery in the a context of increasing normalization on the financial markets and a gradual consolidation of the labour market," the central bank said.
On an annual basis, the Spanish economy grew 0.5 percent in the first quarter, the bank estimated, the first year-on-year expansion in more than two years.
Spain's economy is set to grow by 1.2 percent in 2014 and 1.7 percent in 2015, the Bank of Spain said, confirming an earlier forecast.
Spain emerged gingerly from a two-year downturn in mid-2013 but still suffers from an unemployment rate of nearly 26 percent.
The country managed to avoid an international bailout in mid-2012, a risk that haunted financial markets as the nation's debt soared.
Investors have also taken heart from the European Central Bank's vow in late 2012 to come to the rescue of stricken eurozone members.
Exit door from crisis
Prime Minister Mariano Rajoy's austerity measures and labour market reforms helped to consolidate financial market support further.
Economy Minister Luis de Guindos said he expected the economy to grow by an average of 1.5 percent in 2014 and 2015.
"The goal is to achieve two years in a row of growth, with net job creation, and that will be the exit door from the Spanish crisis," De Guindos said.
Nevertheless, jobs growth will be "clearly insufficient", he said.
Latest revised data showed the unemployment rate in the final quarter of 2013 stood at 25.73 percent.
"A country with an unemployment rate of 26 percent is starting at a terrifying level," de Guindos said.
The Bank of Spain is predicting an unemployment rate still at 25 percent in 2014 and 23.8 percent in 2015.
Spain's lower financing costs, combined with higher tax receipts, would probably allow the Treasury in the next few days to lower its estimate of the money it needs to raise by issuing bonds, the minister said.
Spain has estimated its net financing requirements for this year at €65 billion ($90 billion).
Spain is to publish next week its unemployment data for the first quarter of 2014.