The company, which delivers around 20% of the UK's national newspapers, has said it is targeting the regional market as publishers seek to cut costs.
Included in the contract, which begins on 27 October, will be Southampton's Southern Daily Echo and Bournemouth's Daily Echo. The deal also included several freesheets in Hampshire and Dorset.
Dawson trading director Terry Perry said: "We see regional press distribution as an opportunity for us, it is a win-win.
"We can incorporate the newspapers into our existing deliveries, allowing publishers, which are all looking to cut costs, to eliminate their fleet."
Dawson secures distribution deal with Newsquest
Newspaper distribution firm Dawson News has been awarded a contract to distribute publisher Newsquest's regional titles in Southampton and Bournemouth.