President Eion Willis said members voted to shut down the club at a special meeting on Sunday.
"It was unanimous," Willis said.
"There are two fundamental reasons why, and the most important one was that we are just not relevant in today’s environment."
The club, which has about 400 members, was registered in 1973 but had operated on an informal basis since the late 1950s.
"Back then, there was no such thing as rugby academies," Willis said.
"There were no pathways or age group rugby to higher honours. There was no secondary school competition as we know today.
"We were able to plug some of those gaps over the years. But when you look now, a lot of those things are covered with the arrival of professional rugby.
"The feeling is we have outlived our usefulness, if I could put it bluntly."
The other major reason for closing down is the club has failed to attract new committee members to carry the organisation forward.
Willis said there was still some work to do in order to close.
One of the priorities was to make sure the country colts team continues to operate.
Otago Country Rugby has agreed to take over running the team and holding the annual camp.
The club’s funds will be transferred to the Otago Rugby Football Union.
"Those funds are to be used in line with the Sassenachs’ objectives, as laid out in 1973, and that really is about junior rugby.
"That will be overseen by two nominated members of the Sassenachs to ensure everything is in accordance with the wishes of the members."
Willis hoped the club’s memorabilia would find a new home with the Otago union.
"There are some magnificent photos in our clubrooms [at Forsyth Barr Stadium]. They are very special photos and obviously they won’t go to waste.
"The ORFU may wish to have them because they are all about the history of Otago rugby anyway."
Willis said he felt a pang of sadness but it was a practical decision because the club had been struggling to attract new committee members and was no longer relevant.