Depends on which version you have. Some say to place the cards under the draw pile while others say to place it on the play pile (which is sometimes called the discard pile)
One Way (under the draw pile)
If placing them under the draw pile, the rules don't specify the order when placing them on the bottom of the draw pile, so you're free to choose whatever order you like.
Rules:
- End your Turn
If you have more than 7 cards in your hand at the end of your turn (not including cards on the table) discard extras to the bottom of the draw pile so you only have 7.
It's worded differently in these rules, but the effect is the same:
If you have more than 7 cards in your hand at the end of your turn (not including cards on the table) discard extras to the bottom of the draw pile so you only have 7. If you've run out of cards, take 5 at the start of your next turn.
Scan of those rules
PDF of those rules
The other way (to the play pile)
These rules (branded "Monopoly Millionaire", but they're the only ruleset I can find that gives the alternate play style) say to place them on the play pile (in which case they'd be placed face up like other cards placed there):
Just before the next player’s turn, check how many cards you have left
in your hand.
- More than 7? Throw any extras on the play pile
Both Ways (monopolydealrules.com)
This unofficial site says that the rule is to discard to the discard pile, but references the official rules that say to discard to the bottom of the draw pile:
General summary:
At the end of each player’s turn, they cannot have more than 7 cards in their hand. If they do, they need to discard the excess Monopoly cards into the discard pile in the middle.
Linked rules:
If you have more than 7 cards in your hand at the end of your turn (not including cards on the table) discard extras to the bottom of the draw pile so you only have 7.