This is what I do, and I learned it here on WC from a well respected artist, Larry Seiler. Here is the article: How to make a canvas board
You basically take a piece of hardboard/MDF/masonite (plywood should work too) and glue the canvas to the board using acrylic medium. I've even done this with Fredrix canvas pad sheets (real canvas) with paintings already on them, just like yours.
What I do is position my board on the back of the canvas and mark the corners with charcoal or pencil so I know where to position it later.
Then I spread acrylic gel medium with a brush onto one side of the board. Then I do the same to the back of the canvas inside my imaginary rectangle with the marked corners. (if the board is the same size as the canvas, then you don't have to worry about marking the corners...I've done it that way too).
By the time I'm done that, the board is dry, so I give it another coat. I make sure everything is even with no globs anywhere, and fairly thin since there will me more than enough on the canvas.
Then I positon the wet side of the board to the wet side of the canvas and slide it to match the corners. I place the whole thing face down onto a larger piece of hardboard for a flat surface, then I stand on it!
After that, I carefully flip it over and lightly rub my fingers over the surface to check for bubbles. If there are any bubbles at all, I use a brayer (a rolling pin would do), and I carefully work the bubbles from the inside out. Be carefull you don't cause dents or grooves in the layer of arcylic medium underneath.
When this is dry, I flip it to the back and cut squares from the corners of the overhanging canvas (if any), then I coat the canvas strips with acrylic medium and stretch them over the edges of the board, smoothing everything with my fingers. If there isn't any canvas to wrap over, then I seal the edges of the board with a bit of acrylic gel medium.
Feel free to ask me any questions.