Both country's militaries have been on alert after a brief exchange of fire at the border last Thursday.
The North had threatened to use force to stop propaganda broadcasts by the South, started after two of its soldiers were injured by a landmine.
High-level negotiators have been meeting since Saturday to agree a deal.
Yonhap reported that the deal, to be announced later on Monday, would see North Korea express "regret" over the landmine incident earlier this month.
In return, it said South Korea would stop the loudspeaker broadcasts that were resumed after an 11-year hiatus, in apparent retaliation for the landmine attack.
South and North Korea have agreed a deal to defuse tensions after a series of recent border confrontations, South Korea's Yonhap news agency says.