The team bid $348 million for the job, much less than three other teams that offered to do the work for $377 million to $582 million.
A bid by a fifth team, led by another Spanish firm, was discarded by the authority as non-responsive to its requirements.
The 22-mile segment would be the third section the agency has contracted since 2013, completing most of the $6 billion of construction awards that has been planned over the last four years in the Central Valley.
The initial construction section is to run 122 miles from Madera to Shafter, roughly eight miles less than originally planned. It would include rail bed, bridges, trenches, viaducts and other structures.
The rail would be installed under a separate contract yet to be awarded. The planned work does not include high-voltage electrical systems or signals that would be needed to operate bullet trains.
The Ferrovial team, which includes the Spanish engineering firm Euroestudios and the Houston-based engineering firm Othon, would begin its work just north of the Tulare-Kings county line and continue south to the northern border of Shafter.
The contract would include construction of viaducts, highway work, wildlife crossings and the relocation of four miles of existing Burlington Northern Sante Fe track.
The first construction contract in the Central Valley, covering 29 miles through Fresno, is about two years behind schedule. So far, a bridge over the Fresno River is the only major structure underway. The authority has said it will make up any delays by moving more quickly in the future.
"We continue to attract world-leading design and construction firms who want to be a part of high-speed rail in California," said Jeff Morales, chief executive of the rail authority.
"People are already and will continue to see major construction projects underway on over 100 miles of infrastructure in the Central Valley as we move this program forward," Morales said.
The entire 122-mile section was originally planned to be completed by next year, when federal grants made under the Obama administration stimulus act are set to expire and might have to be forfeited. But at least some of that work has slipped into 2018 or beyond.
It is becoming increasingly difficult for the state to spend all of the roughly $2 billion in stimulus money by the federal deadline of Sept. 30, 2017.
The Spanish team, led by Ferrovial's U.S. unit, is expected to be selected by the authority's board at a meeting later this month, allowing a formal contract to be negotiated by its staff. The contract process began in November 2014, about 14 months ago.
Ferrovial has won extensive work in the U.S., including a contract late last year to rebuild a section of interstate highway in Atlanta.
The company outbid teams led by Salini Impregilo, Dragados and Tutor Perini. Dragados and Tutor Perini won two earlier bullet train contracts.
The Ferrovia bid came in under the estimate that the authority made in 2014, when it projected the segment would cost $700 million to $900 million, prior to the decision to eliminate eight miles of track from the contract.
In its announcement Tuesday, the authority said it was expecting the contract bids to fall between $400 million and $500 million.