When the glue has dried securely, test fit the assembled back of your walnut chair into the seat section. You may need to sand or file the edges of the seat base in order to get a the back to fit into the base so that it can be glued. The better the fit, the stronger your chair will be. The chair will also gain some strength from the upholstery which will be glued into the chair back.
When the back of the chair will fit securely into the seat section, apply glue around the line where the back meets the seat and glue the pieces together, clamping them or holding them with small weights until the glue has dried.