To export your Outlook emails, contacts & other data to Gmail there are two methods you can use. One is long can complicated manual method and other is an easy and fast method using third-party software.
In the manual method first, you need to export your Outlook mailboxes and folders to a PST file using Import/Export option in MS Outlook application and then use a tool called GSSMO from Google to import data from PST file in your Gmail Account.
In the second method, you can use vMail OST File Converter Tool to directly export your Outlook data from OST file to Gmail.
More Details- Import OST file data into Gmail