Mariner earned 35 caps for England between 1977 and 1985 and scored 13 times for his country.
He spent the best part of his career at Ipswich, where he scored 139 goals in 339 games and was a member of their team that won the FA Cup in 1978 and the UEFA Cup in 1981.
Mariner left Ipswich for Arsenal in 1984 and went on to make 70 appearances for the Gunners before joining Portsmouth in 1986.
A statement from Mariner’s family, posted on his Twitter account, read: “We regretfully inform you that Paul passed away peacefully on July 9 surrounded by his family, after a brief battle with brain cancer.
“We would like to thank all the people who came to see him through his illness for their support and the messages that were sent to him, they meat a great deal to him and us.
“A special thank you must go to the NHS and the unbelievable care that he received when he most needed it and for that we, as a family, will be forever in your debt.
“Paul lived a full life and was fortunate enough to represent a group of fantastic football clubs as well as his country, all of which meant the world to hm.
“Anyone who knew Paul will attest to his fantastic sense of humour, his passion for life and his work. He will be sorely missed by everyone who was ever around him and by those most close to him.”
A tweet from the England team's account read: "We're sad to have learned that Paul Mariner, who made 35 appearances for the Three Lions, has passed away at the age of 68.
"Mariner represented England between 1977 and 1985, scoring 13 goals. Our thoughts and sympathies are with his family, friends and former clubs.”
Arsenal said: “We were saddened to hear of the passing of former Arsenal striker Paul Mariner. Everybody at Arsenal sends their sincere condolences to Paul’s friends and family at this time.”
A tweet from Ipswich read: "We are devastated to hear the news of the passing of Town legend Paul Mariner at the age of 68. The thoughts of everyone at Ipswich Town are with Paul's family and friends at this sad time.”