Since all of the other answers here use jQuery, I'll add one done with vanilla js.
To do this, we're going to need to use a javascript closure. This is used so that on completion of the fade-out, we have (a) the element just faded and (b) which is far more important, an index into the originalStrings array. (B) is the more important here, because the target element is something the animate code already has - we could easily pass the original element to the callback function. However, we really need the index or the string that corresponds to each element. The closure gives a means to do so.
The following code will fade-out all/any matching elements and then perform a fade-in after changing the text.
Using the equations found here: Math: Ease In, ease Out a displacement using Hermite curve with time constraint we can then set about making some code that will perform a smooth fade/move/scale pitch/volume slide etc, etc. I did this an ended up a few functions that facilitate simple animations. I've included minified versions of them below, for an all-in-one complete solution that relies on no other resources.
<!DOCTYPE html>
<html>
<head>
<script>
"use strict";
window.addEventListener('load', onDocLoaded, false);
function onDocLoaded()
{
document.getElementById('goBtn').addEventListener('click', onButtonClick, false);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// animation stuff
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////
function cubicHermite(a,b,d,e,c){var g=a*a,f=g*a;return(2*f-3*g+1)*b+(f-2*g+a)*e+(-2*f+3*g)*d+(f-g)*c}
function interp(a,b,d,e,c){var g,f;f=e/(a/2+b+d/2);g=f*a/2;f*=b;return c<=a?cubicHermite(c/a,0,g,0,f/b*a):c<=a+b?g+f*(c-a)/b:cubicHermite((c-a-b)/d,g+f,e,f/b*d,0)}
function linear(a){return a}
function cubic(a){return interp(0.35,0.3,0.35,1,a)}
function doAnimStep(a,b,d,e,c){a<=b?(setTimeout(function(){doAnimStep(a,b,d,e,c)},d),e(a/b),a++):void 0!=c&&null!=c&&c()}
function doAnim3(totalMs, stepCallbackFunc, doneCallbackFunc)
{
var stepDelay = 1000 / 60.0; // set anim to 60 fps
var numSteps = (totalMs / stepDelay)>>0;
setTimeout( doAnim3TimeoutCallback, stepDelay );
function doAnim3TimeoutCallback()
{
doAnimStep(0, numSteps, stepDelay, stepCallbackFunc, doneCallbackFunc);
};
}
function animFadeOut(elem, callback){ doAnim3(500,function(raw){elem.style.opacity=1-cubic(raw)},callback); }
function animFadeIn(elem, callback) { doAnim3(500,function(raw){elem.style.opacity=cubic(raw)},callback); }
////////////////////////////////////////////////////////////////////////////////////////////////////////////////
var replacementStrings = [ "replacement 1", "I'm next", "mee too", "fourth item" ];
function onButtonClick(evt)
{
var originalStrings = [];
var targetLiElems = document.querySelectorAll('.menu-wrapper > ul > li');
for (var i=0,n=targetLiElems.length;i<n;i++)
{
var curElem = targetLiElems[i];
originalStrings.push(curElem.innerText);
animFadeOut(curElem, createFunc(i) );
}
function createFunc(i)
{
return function(){ var curElem = targetLiElems[i]; curElem.innerText = replacementStrings[i]; animFadeIn(curElem); };
}
}
</script>
<style>
</style>
</head>
<body>
<button id='goBtn'>Change the text</button>
<div class="menu-wrapper">
<ul>
<li>WORD1</li>
<li>WORD2</li>
<li>WORD3</li>
<li>WORD4</li>
</ul>
</div>
</body>
</html>