"commission a project" is correct and usable in written English.
You can use this phrase when you would like to assign responsibility for carrying out a task or project. For example: "The board appointed me to commission a project to reduce carbon emissions in the company."
Here he opened negotiations with the Transcaucasian Federation of the three republics, Armenia, Georgia, and Azerbaidjan, with the view of raising a loan in order to carry out the proposals of the Commission—a project which, he tells us, later failed to mature.
A phenomenon of recent years has been the turnkey or package contract, in which the contractor undertakes to finance, design, specify, construct, and commission a project in its entirety.
During the railways budget speech on Tuesday, Railways Minister Pawan Kumar Bansal said that this year the government would commission a project linking Harmuti region in the northeastern state of Assam to Naharlagun in Arunachal Pradesh.
To commission a project well you have to predict what a Controller will need a year or more in advance and what an audience will respond to, not always the same thing; and do this on the evidence of a pitch and a few personalities.
Last year, Daimler AG's board commissioned a project staffed by executives from around the world to rethink leadership standards.
The UK Chartered Institute of Building Service Engineers subsequently commissioned a project to extract a sub-set of these data for inclusion in Guide A, Section 3.
Determined to build a low-cost design and manufacturing platform, Paliwal in 2008 commissioned a project that took an entirely new approach.
We've commissioned a project by Tracie Morris called "Grown Over Ivy," which explores the relationship of Yale to the community.
After she saw the cellphone video of Neda Agha-Soltan, killed a year ago in Tehran during the protests following the disputed Iranian presidential contest, she commissioned a project to track down the back story.
Every year BBC Radio Scotland commissions a project called SoundTown.
