After a gradual return to growth, "2014 has been the year of recovery and 2015 will be the year when our economy really takes off," Rajoy told a news conference.
Spain technically exited recession in mid-2013 after five years of economic turbulence but the unemployment rate remains extremely high at 24 percent.
Rajoy attributes the recovery to tough budget cuts that he said were necessary to strengthen the public finances. But the measures have sparked fierce popular protests.
The new left-wing anti-austerity party Podemos has overtaken Rajoy's conservative Popular Party in some opinion polls ahead of Spain's next general election due in November.
Rajoy said Spain was now enjoying "solid" growth, forecast at up to 1.4 percent in 2014.
The leader of the opposition Socialist Party, Pedro Sanchez, in his own end-of-year news conference insisted the crisis was not over for ordinary Spaniards, however.
"It is indecent and unjust for a government to declare an end to the crisis while it continues to cut education and public healthcare," Sanchez said.
"Until we recover the levels of unemployment and social protection we had prior to the crisis, I ask Mr Rajoy not to use the word recovery in vain."