.gradient {
  background-image: linear-gradient(to right, olive, green);
  transition: background-image 0.5s linear;
}
.gradient:hover {
  background-image: linear-gradient(to right, green, purple);
}

<div class="box"></div>

.box {
    max-width: 400px;
    height: 200px;
    background: linear-gradient(to right, olive, green, purple);
    background-size: 200%;
    transition: background-position .5s;    
}
.box:hover {
    background-position: 100% 0;    
}

<div class="box"></div>

.box {
    max-width: 400px;
    height: 200px;
    background: olive linear-gradient(to right, rgba(0,255,0,0), rgba(0,255,0,.5));
    transition: background-color .5s;    
}
.box:hover {
    background-color: purple;    
}

<div class="box"></div>

.box {
    max-width: 400px; height: 200px;
    background: linear-gradient(to right, olive, green);
    position: relative;
    z-index: 0;    
}
.box::before {
    content: '';
    position: absolute;
    left: 0; top: 0; right: 0; bottom: 0;
    background: linear-gradient(to right, green, purple);
    opacity: 0;    
    transition: opacity .5s;
    z-index: -1;
}
.box:hover::before {
    opacity: 1;    
}