If your data may contain multi-byte sequences (not a plain ASCII sequence) and your browser has TextDecoder, then you should use that to decode your data (specify the required encoding for the TextDecoder):

var u8 = new Uint8Array([65, 66, 67, 68]);
var decoder = new TextDecoder('utf8');
var b64encoded = btoa(decoder.decode(u8));

If you need to support browsers that do not have TextDecoder (currently just IE and Edge), then the best option is to use a TextDecoder polyfill.

If your data contains plain ASCII (not multibyte Unicode/UTF-8) then there is a simple alternative using String.fromCharCode that should be fairly universally supported:

var ascii = new Uint8Array([65, 66, 67, 68]);
var b64encoded = btoa(String.fromCharCode.apply(null, ascii));

And to decode the base64 string back to a Uint8Array:

var u8_2 = new Uint8Array(atob(b64encoded).split("").map(function(c) {
    return c.charCodeAt(0); }));

If you have very large array buffers then the apply may fail with Maximum call stack size exceeded and you may need to chunk the buffer (based on the one posted by @RohitSengar). Again, note that this is only correct if your buffer only contains non-multibyte ASCII characters:

function Uint8ToString(u8a){
  var CHUNK_SZ = 0x8000;
  var c = [];
  for (var i=0; i < u8a.length; i+=CHUNK_SZ) {
    c.push(String.fromCharCode.apply(null, u8a.subarray(i, i+CHUNK_SZ)));
  }
  return c.join("");
}
// Usage
var u8 = new Uint8Array([65, 66, 67, 68]);
var b64encoded = btoa(Uint8ToString(u8));