datepicker-localize.js

jQuery('.datepicker').datepicker({
    // Show the 'close' and 'today' buttons
    showButtonPanel: true,
    closeText: objectL10n.closeText,
    currentText: objectL10n.currentText,
    monthNames: objectL10n.monthNames,
    monthNamesShort: objectL10n.monthNamesShort,
    dayNames: objectL10n.dayNames,
    dayNamesShort: objectL10n.dayNamesShort,
    dayNamesMin: objectL10n.dayNamesMin,
    dateFormat: objectL10n.dateFormat,
    firstDay: objectL10n.firstDay,
    isRTL: objectL10n.isRTL,
});

datepicker-localize.php

<?php

add_action( 'admin_enqueue_scripts', 'admin_print_js' );

public function admin_print_js() {
    global $wp_locale;
 
    //add the jQuery UI elements shipped with WP
    wp_enqueue_script( 'jquery' );
    wp_enqueue_script( 'jquery-ui-datepicker' );
 
    //add our instantiator js
    wp_enqueue_script( 'myplugin-admin', MYPLUGIN_URI . "js/myplugin-admin.js", array( 'jquery-ui-datepicker' ) );
 
    //localize our js
    $aryArgs = array(
        'closeText'         => __( 'Done', UNIQUE_TEXT_DOMAIN ),
        'currentText'       => __( 'Today', UNIQUE_TEXT_DOMAIN ),
        'monthNames'        => strip_array_indices( $wp_locale->month ),
        'monthNamesShort'   => strip_array_indices( $wp_locale->month_abbrev ),
        'monthStatus'       => __( 'Show a different month', UNIQUE_TEXT_DOMAIN ),
        'dayNames'          => strip_array_indices( $wp_locale->weekday ),
        'dayNamesShort'     => strip_array_indices( $wp_locale->weekday_abbrev ),
        'dayNamesMin'       => strip_array_indices( $wp_locale->weekday_initial ),
        // set the date format to match the WP general date settings
        'dateFormat'        => date_format_php_to_js( get_option( 'date_format' ) ),
        // get the start of week from WP general setting
        'firstDay'          => get_option( 'start_of_week' ),
        // is Right to left language? default is false
        'isRTL'             => $wp_locale->is_rtl,
    );
 
    // Pass the localized array to the enqueued JS
    wp_localize_script( 'myplugin-admin', 'objectL10n', $aryArgs );
}

/**
 * Format array for the datepicker
 *
 * WordPress stores the locale information in an array with a alphanumeric index, and
 * the datepicker wants a numerical index. This function replaces the index with a number
 */
function strip_array_indices( $ArrayToStrip ) {
    foreach( $ArrayToStrip as $objArrayItem) {
        $NewArray[] =  $objArrayItem;
    }
 
    return( $NewArray );
}

/**
 * Convert the php date format string to a js date format
 */
function date_format_php_to_js( $sFormat ) {
    switch( $sFormat ) {
        //Predefined WP date formats
        case 'F j, Y':
            return( 'MM dd, yy' );
            break;
        case 'Y/m/d':
            return( 'yy/mm/dd' );
            break;
        case 'm/d/Y':
            return( 'mm/dd/yy' );
            break;
        case 'd/m/Y':
            return( 'dd/mm/yy' );
            break;
     }
}