Both Beeslack and Currie Woods will have more finance for protection as a result of the agreement, announced today.
It is understood expanding both areas could be one way of raising the profiles of the two zones and attracting more visitors.
Expansion by 2050 is one of the trust's pledges. The scheme was launched by Miss Scotland Nicola Mimnagh.
She said: "At this time of year, when the leaves on the trees are changing to a wonderful mix of gold, orange and red, Scotland's woodlands are at their most beautiful.
"I'm sure the money raised by postcode lottery players will help to protect Scotland's native woodlands for generations to come."