I tried sample one for your question
import UIKit
class ViewController: UIViewController {
@IBOutlet var webViewDynamicHeight: UIWebView!
var horizontalConstraint : NSLayoutConstraint!
var verticalConstraint: NSLayoutConstraint!
var widthConstraint : NSLayoutConstraint!
var heightConstraint : NSLayoutConstraint!
override func viewDidLoad() {
    super.viewDidLoad()
    // Do any additional setup after loading the view, typically from a nib.
    webViewDynamicHeight.loadRequest(NSURLRequest(URL: NSURL(string: "https://www.google.de/intl/de/policies/terms/regional.html")!))
}
override func didReceiveMemoryWarning() {
    super.didReceiveMemoryWarning()
    // Dispose of any resources that can be recreated.
}
func webViewDidFinishLoad(webView: UIWebView) {
    let height:CGFloat = webView.scrollView.contentSize.height
    print("The webView height is -: \(height)")
    let width:CGFloat = webView.scrollView.contentSize.width
    print("The webView height is -: \(width)")
    horizontalConstraint = NSLayoutConstraint(item:webView, attribute: NSLayoutAttribute.CenterX, relatedBy: NSLayoutRelation.Equal, toItem: view, attribute: NSLayoutAttribute.CenterX, multiplier: 1, constant: 0)
    webView.addConstraint(horizontalConstraint)
    verticalConstraint = NSLayoutConstraint(item: webView, attribute: NSLayoutAttribute.CenterY, relatedBy: NSLayoutRelation.Equal, toItem: view, attribute: NSLayoutAttribute.CenterY, multiplier: 1, constant: 0)
    webView.addConstraint(verticalConstraint)
    widthConstraint = NSLayoutConstraint(item: webView, attribute: NSLayoutAttribute.Width, relatedBy: NSLayoutRelation.Equal, toItem: nil, attribute: NSLayoutAttribute.NotAnAttribute, multiplier: 1, constant: 100)
    widthConstraint.constant = width
    webView.addConstraint(widthConstraint)
    heightConstraint = NSLayoutConstraint(item: webView, attribute: NSLayoutAttribute.Height, relatedBy: NSLayoutRelation.Equal, toItem: nil, attribute: NSLayoutAttribute.Height, multiplier: 1.0, constant: height)
    heightConstraint.constant = height
    webView.addConstraint(heightConstraint)
}
}