Google gives thumbs-up on placing your local reviews from Yelp, Google Maps and others on your own website
The only exception here: Make sure not to mark up those copied reviews with review structured data and schema. That would be against Google's guidelines.
You’ve probably all seen websites that showcase the reviews their customers have left for them on Yelp, Google Maps and other third-party websites. According to John Mueller, a Google webmaster trends analyst, it is perfectly OK with Google’s webmaster guidelines to take some of those reviews and highlight them on your company website. The only thing he warns you not to do is use review structured data on those reviews on your own website.
John Mueller said this on Twitter:
John said, “]F]rom a Google SEO point of view, I don’t see a problem with that,” i.e., using these reviews on your website. But he said you probably won’t rank better or worse because you did. Google will primarily look at the unique content on the page, as opposed to the copied reviews.
In addition, John explained that it is against their guidelines to mark up reviews from third-party sites on your own website. Google said the markup is reserved for reviews “directly produced by your site” and not copied from sites like Yelp, Google Maps and others — even if it is about your company.
So feel free to add to your own site reviews you are proud of that are left by customers on Yelp, Google Maps or other review sites. If you produce apps, consider using the iTunes and Android reviews. If you have quality customer testimonials, use those as well.