Animating Linear Gradient using CSS

Dynamic implementation of Dave's answer:

:root{
    --overlay-color-1: #ff0000;
    --overlay-color-2: #0000ff;
    --anim-duration: 2s;
}

#gradient {
    opacity: 0.8;
    background: none;
}

#gradient:after,
#gradient:before {
    content: '';
    display: block;
    position: absolute;
    top: 0; bottom: 0; left: 0; right: 0;
}

#gradient:before {
    background: linear-gradient(135deg, var(--overlay-color-2) 0%, var(--overlay-color-1) 100%);
    animation: OpacityAnim var(--anim-duration) ease-in-out 0s infinite alternate;
}

#gradient:after {
    background: linear-gradient(135deg, var(--overlay-color-1) 0%, var(--overlay-color-2) 100%);
    animation: OpacityAnim var(--anim-duration) ease-in-out calc(-1 * var(--anim-duration)) infinite alternate;
}

@keyframes OpacityAnim {
    0%{opacity: 1.0}
    100%{opacity: 0.0}
}
<div id="gradient"></div>

Please try this code:

#gradient
{
    height:300px;
    width:300px;
    border:1px solid black;
    font-size:30px;
    background: linear-gradient(130deg, #ff7e00, #ffffff, #5cff00);
    background-size: 200% 200%;

    -webkit-animation: Animation 5s ease infinite;
    -moz-animation: Animation 5s ease infinite;
    animation: Animation 5s ease infinite;
}

@-webkit-keyframes Animation {
    0%{background-position:10% 0%}
    50%{background-position:91% 100%}
    100%{background-position:10% 0%}
}
@-moz-keyframes Animation {
    0%{background-position:10% 0%}
    50%{background-position:91% 100%}
    100%{background-position:10% 0%}
}
@keyframes Animation { 
    0%{background-position:10% 0%}
    50%{background-position:91% 100%}
    100%{background-position:10% 0%}
}
<html>
<div id="gradient">
  Hello
</div>
</html>