I don't have my research at my fingertips so going off of memory here, and your situation may be different based on your applicable corporate statute and bylaws...

When I last looked into this we concluded it was not legally necessary for the corporate secretary or meeting chair to sign the minutes but it's a good idea, for purposes of version control, avoiding disputes and for having definitive versions for future reference. 

Ultimately, it's the corporate secretary's responsibility to maintain the minutes (as per the applicable corporate statute), and I think their signature is useful for evidencing that approval and the other reasons mentioned above. 

As for the meeting chair, I see their signature as evidence that the minutes were duly approved by the body but some chairs are reluctant to sign if they did not attend the meeting in question and sometimes they are no longer available to sign.  So I don't think their signature is essential but I do think it's a good practice for the reasons above.  I'm pretty sure it's still the norm too.  

As for getting signatures in this electronic era, I think most jurisdictions allow for electronic signatures.  As discussed on another thread, many believe it's a good idea to continue to maintain hard copy minutes, so we get electronic signatures and then periodically print the minutes for insertion into the minute book when it's convenient.