Haven't been able to find anything that formats the select2 control properly for Bootstrap 4 so I complied this sccs file to do so. Includes form validation styling but only includes form-control-lg and form-control classes. Will add the form-control-sm later.

select2-bootstrap4.scss

/**
* Feel free to change the colors below.
* Need to update this this to handle form-control-sm.
* Ensure you load these customizations after the select2 css file in order to override them.
*
* This is an example of the input and jQuery you need
*
* <select id="select-example" class="custom-select form-control" style="width:100%">
    <option value="">--Add Value--</option>
</select>
*
*
$('#select-example').select2({
    width: 'resolve'
})
*
*
*/

.was-validated .custom-select:invalid+.select2 .select2-selection {
    border-color: $danger;
}

.was-validated .custom-select:valid+.select2 .select2-selection {
    border-color: $success;
}

*:focus {
    outline: 0px;
}

span.select2-selection.select2-selection--single:focus {
    color: $input-color;
    background-color: $input-bg;
    border-color: $input-border-color;
    outline: 0;
    @include form-control-focus();
}

.form-control-lg+.select2 .select2-selection.select2-selection--single {
    height: $input-height-lg;
    padding: $input-padding-y-lg $input-padding-x-lg;
    @include font-size($input-font-size-lg);
    line-height: $input-line-height-lg;
    @include border-radius($input-border-radius-lg);
}

.form-control+.select2 .select2-selection.select2-selection--single {
    height: $input-height;
    padding: $input-padding-y $input-padding-x;
    @include font-size($input-font-size);
    line-height: $input-line-height;
    @include border-radius($input-border-radius);
}

.form-control-lg+.select2-container--default .select2-selection--single .select2-selection__arrow {
    height: $input-height-lg;
}

.form-control+.select2-container--default .select2-selection--single .select2-selection__arrow {
    height: $input-height;
}

.select2-container--default .select2-selection--single {
    border: $input-border-width solid $input-border-color;
}

.select2-container .select2-selection--single .select2-selection__rendered {
    padding-left: 0;
}

.form-control-lg+.select2-container--default .select2-selection--single .select2-selection__rendered {
    line-height: $input-line-height-lg;
}

.form-control+.select2-container--default .select2-selection--single .select2-selection__rendered {
    line-height: $input-line-height;
}