The 114-mile transmission line will strengthen electrical interconnection between California and Arizona.
Abengoa CEO Santiago Seage said: "This new award will help us to accelerate our development in the power transmission market in the US, where we expect to continue leveraging our global expertise in order to become a significant player in development, engineering, construction and maintenance of large transmission assets."
The project, which is planned to be commissioned in 2020, is estimated to cost approximately $300m.
Abengoa will manage construction, operation and maintenance of the transmission line.
Starwood Energy managing director Himanshu Saxena said: "We are looking forward to making this project a success for all stakeholders and to helping California meet its ambitious energy objectives."