Meath will ply their trade in Division 2 of the Allianz Football League next season, while Down are demoted after both recorded wins this afternoon.
With snow having put paid to the original date for these games, all four teams found themselves in action on a weekend where they would have hoped to be contesting the final in Croke Park
Meath claimed a 1-12 t 0-7 win over neighbours Louth, who had already been relegated.
The Royals finished strongly as the Wee County pushed them hard throughout.
Donal Lenihan was central to this Meath victory, scoring a vital 1-1 in the closing stages.
Earlier, Louth edged a 0-4 to 0-3 interval lead, in a game where the visitors finished with 14 men after Tommy Durnin picked up a second yellow card late on.
Shane McEntee levelled matters on 40 minutes before a Lenihan point handed Meath the lead for the first time since the opening minute and they drove on.
At Pairc Esler, a 2-11 to 1-11 win over Tipperary failed to keep Down in the second tier.
Leading 1-7 t 0-6 at half-time, the Mourne County looked good, but the lead could have been greater - firing five wides, with Sean Dornan scoring an early goal.
Tipperary claimed just two points in a 20-minute spell before the break with Michael Quinlivan and Kevin Fahey on target.
Tipperary drove ahead entering the final quarter, but a Donal O'Hare penalty goal saw the hosts to victory.
The visitors finished with 14 men, after Robbie Kiely's second yellow card in the 65th minute.