1 Kings 1:35
Then ye shall come up after him, that he may come and sit upon my throne; for he shall be king in my stead: and I have appointed him to be ruler over Israel and over Judah. Then ye shall come up after him, that he may come and sit upon my throne; for he shall be king in my stead: and I have appointed him to be ruler over Israel and over Judah.
David appointed Solomon to sit on his throne and be king in his place as ruler over Israel and over Judah, publicly confirming him as his appointed successor. His appointment carried out God's choice behind Solomon's succession and the divine direction that Solomon should succeed him. In acting on that direction David abdicated in Solomon's favor, and Solomon was immediately anointed and proclaimed king.
The order is that after the anointing the people are to come up following Solomon so that he may come and take his seat on the throne in a public transfer of royal authority. David gave this order decisively during Adonijah's rebellion, and the public transfer defeated Adonijah's attempt to seize the throne. By this decisive action the kingdom was kept from passing to a usurper.