The match is scheduled to be played at Kintyre Park on Wednesday 11 July with a 6pm kick-off, and will form part of Ton's pre-season fixture list.
The Argyll club, who finished fourth in the Scottish Amateur Football League Premier 2 last season, are represented only by players aged 19 to 24 and Ton have advised that they will send a squad replete with youth prospects and also some first-team players.
The tie rekindles a long-standing relationship between the clubs that stretches back as far as 1913 - when 1,500 fans watched Morton triumph 2-1 at Kintyre Park.
Local paper the Campbeltown Courier reported at the time that 'The Greenock club brought down a fine team, in which four internationalists figured, greatly overshadowing the local 11 for talent'.
Ton officials and players are to have travel taken care of and will be treated to a dinner after the match to mark the occasion.
Chairman Douglas Rae told the Tele: "They are making a big thing of it - in a way I hope we don't go there and beat them 10-0!
"It is like a missionary journey and we are happy to take part. They will be holding a dinner afterwards and I will be making a presentation to the club.
"I believe they get money for staging the game but that is beside the point.
"We have an existing relationship with Campbeltown and it is a big occasion. This will be our fifth visit - our last was in 2004 - while Hamilton Academical and Queen's Park have also played there.
"But they contacted me to tell me that they wanted Morton to play this match."
Rae concedes it is regrettable the tie has had to be scheduled for a Wednesday night as the number of travelling fans is likely to be affected.
However, the Cappielow chief says it was the only date available as the First Division club look to finalise their preparations for the new campaign.
Rae said: "We did not have a Saturday available to go and play this match so it has had to be Wednesday 11 July, with a 6pm kick-off.
"That is not ideal for our supporters.
"The people at Campbeltown have said they hope there will be a good turnout and hopefully we will have a few along.
"I have been up north in the Highlands when we played teams up there and there were a number of supporters at those games, hopefully a few will be willing to travel this time too."