The following will work:
val sourcesJar by creating(Jar::class) {
    dependsOn(JavaPlugin.CLASSES_TASK_NAME)
    classifier = "sources"
    from(sourceSets["main"].allSource)
}
val javadocJar by creating(Jar::class) {
    dependsOn(JavaPlugin.JAVADOC_TASK_NAME)
    classifier = "javadoc"
    from(tasks["javadoc"])
}
artifacts {
    add("archives", sourcesJar)
    add("archives", javadocJar)
}
A complete build.gradle.kts would look like this:
plugins {
    kotlin("jvm") version "1.2.71"
}
repositories {
    mavenCentral()
}
dependencies {
}
tasks {
    val sourcesJar by creating(Jar::class) {
        dependsOn(JavaPlugin.CLASSES_TASK_NAME)
        classifier = "sources"
        from(sourceSets["main"].allSource)
    }
    val javadocJar by creating(Jar::class) {
        dependsOn(JavaPlugin.JAVADOC_TASK_NAME)
        classifier = "javadoc"
        from(tasks["javadoc"])
    }
    artifacts {
        add("archives", sourcesJar)
        add("archives", javadocJar)
    }
}