The party said Mr Sobel, who represents Moortown on Leeds Council, was an overwhelming winner at hustings attended by local members.
The Parliamentary seat is currently held by Greg Mulholland for the Liberal Democrats.
Mr Sobel, who also runs the community project Social Enterprise Yorkshire and the Humber, said: “My priorities are simple: good jobs and high quality education for the people of Leeds North West. We need to be working to bring green manufacturing and high tech jobs to Leeds and we need to campaign for high quality universal state education including cutting the crippling tuition fees pushing our students and graduates into debt.
“I’m confident we can win here, but to do so we need to get out to meet and listen to as many voters as possible. That hard work starts right away.”