Cross-browser method

// Create Base64 Object
var Base64={_keyStr:"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=",encode:function(e){var t="";var n,r,i,s,o,u,a;var f=0;e=Base64._utf8_encode(e);while(f>2;o=(n&3)<<4|r>>4;u=(r&15)<<2|i>>6;a=i&63;if(isNaN(r)){u=a=64}else if(isNaN(i)){a=64}t=t+this._keyStr.charAt(s)+this._keyStr.charAt(o)+this._keyStr.charAt(u)+this._keyStr.charAt(a)}return t},decode:function(e){var t="";var n,r,i;var s,o,u,a;var f=0;e=e.replace(/[^A-Za-z0-9+/=]/g,"");while(f>4;r=(o&15)<<4|u>>2;i=(u&3)<<6|a;t=t+String.fromCharCode(n);if(u!=64){t=t+String.fromCharCode(r)}if(a!=64){t=t+String.fromCharCode(i)}}t=Base64._utf8_decode(t);return t},_utf8_encode:function(e){e=e.replace(/rn/g,"n");var t="";for(var n=0;n127&&r<2048){t+=String.fromCharCode(r>>6|192);t+=String.fromCharCode(r&63|128)}else{t+=String.fromCharCode(r>>12|224);t+=String.fromCharCode(r>>6&63|128);t+=String.fromCharCode(r&63|128)}}return t},_utf8_decode:function(e){var t="";var n=0;var r=c1=c2=0;while(n191&&r<224){c2=e.charCodeAt(n+1);t+=String.fromCharCode((r&31)<<6|c2&63);n+=2}else{c2=e.charCodeAt(n+1);c3=e.charCodeAt(n+2);t+=String.fromCharCode((r&15)<<12|(c2&63)<<6|c3&63);n+=3}}return t}}

// Define the string
var string = 'Hello World!';

// Encode the String
var encodedString = Base64.encode(string);
console.log(encodedString); // Outputs: "SGVsbG8gV29ybGQh"

// Decode the String
var decodedString = Base64.decode(encodedString);
console.log(decodedString); // Outputs: "Hello World!"


References