You can achieve this with the Bevel modifier. Enable
Tab into edit mode and select the corners you want to curve. Press CtrlG followed by A or click Mesh -> Vertices -> Vertex Groups -> Assign to New Group to assign them to a new vertex group.
Tab back to object mode and add a Bevel modifier.
Enable Only Vertices set Limit Method to Vertex Group and adjustselect the vertex group you just created (by default it will be named Group). Adjust Segments and Width to meet your needs.

