Selleys Liquid Nails Mirror Metal Glass is ideal for this job. You can also use Mirror Metal Glass to seal around the edges of the mirror once it has fully cured behind the mirror.
We recommend allowing the adhesive to fully cure for about 7 days before sealing around the edges of the mirror.
If you wanted to use a different colour around the edge of the mirror you can use Selleys Wet Area Silicone or Roof & Gutter Silicone.