The company is running a special timetable until 12 August and between 29 August to 9 September.
It includes trains starting earlier and ending later on some routes and extra carriages being added to services.
The rail firm added that on Monday London Bridge platforms 1-6 would be exit only between 18:00 BST and 22:00 BST.
The company said Monday would be the busiest day, with 50,000 people expected to attend the equestrian cross-country event at Greenwich Park.
Southeastern also has 1,000 additional temporary staff to assist passengers over the summer.
Alison Nolan, from the firm, said: “From this weekend, our services will be extremely busy.
“Queues are to be expected at many London terminal stations.
“We recommend passengers travelling during Games-time check to see how their journey is likely to be affected.”
The rail firm added that only essential maintenance on its network would be carried out during the Games.