She will now become co-chairman with Sir John Madejski, who has been with the Berkshire club since 1990.
Previous majority shareholder Anton Zingarevich left the club's board in June, but Madejski had been looking for new investment since last year.
In a statement, Madejski said: "I cannot speak highly enough of our new partners from the time we have spent together so far."
The amount of money involved in the takeover has not yet been disclosed.
But, under the agreement, Sasima and Khun Sumrith Thanakarnjanasuth have each bought 25% of the club.
The other 50% of the shareholding in the club has been bought by Khun Narin Niruttinanon.
Two other Thai members of the consortium will also join the club's board, but Nigel Howe will remain as chief executive.
"I have owned this great club for almost a quarter of a century and it has given me some of the greatest memories of my life," Madejski added.
"I am incredibly proud of the success we have enjoyed both on and off the pitch.
"There are reasons to be optimistic on many fronts, and we now move forward with a renewed vigour and high hopes for a bright new future."
Reading face Sheffield Wednesday at Hillsborough to kick-off the new era and are sitting sixth before that game.