To clear the Google Web History, sign into your Google account and then go to https://www.google.com/history. You can also go to this page by choosing the Account Settings option from the pull down menu at the right top corner of the Google products like Google.com, Gmail and so on.
If you are choosing the second option, scroll down to the Services header and then click on Go to web history link. If the web history is enabled, it will display a list of all the recent searches and the sites you have visited. You have to click Remove the web history button and then OK button to delete it.
By doing this, you are pausing the web history feature so that it will not track your searches anymore. You can click the Resume button to start it again. This way you can control what Google should monitor and retain your privacy.