The Spanish double world champion was set to purchase the WorldTour licence to enable the team to continue racing in 2014, current sponsors Euskaltel said.
"The negotiations will be completed in the next few weeks and will culminate in the purchase of the company (Basque Cycling Pro Team), which owns the team, by Fernando Alonso," the statement said.
Euskaltel-Euskadi are one of Spain's two teams in the WorldTour, cycling's top league.
Led by Spain's Samuel Sanchez, the 2008 Olympic road-race champion, they had looked likely to fold at the end of the season after 17 years after co-sponsors failed to provide promised funding in 2013.
No financial details were given of Alonso's deal but Spanish website El Periodico said the Ferrari driver had some six million euros available to spend on the cycling team.
The Basque squad are currently taking part in the Vuelta, the country's Grand Tour.
Comprised mostly of Basque riders, telecommunications company Euskaltel surprisingly announced they would no longer support the team, in part down to co-sponsors opposing the decision to allow more non-local professionals into the squad, not helped by Spain's economic crisis.
Much like Basque football team Athletic Bilbao, Euskaltel-Euskadi had come to represent the heartland of Spanish cycling and was widely regarded as one of the top teams on the Tour.
But they have never won a Grand Tour, which will surely be the focus of Alonso and his advisers for the coming seasons.