All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
In principle it is permissible to congratulate both spouses on the occasion of consummating their marriage. The evidence is that Anas narrated that when the Prophet married Zaynab 'Aa’ishah asked him: "How did you find your wife, may Allaah bless [her for ] you." [Al-Bukhari] Moreover, when a person married, the Prophet supplicated for him saying: "May Allaah bless you, and may His Blessings be on you, and join you two upon virtue." [Ahmad] Of course this is in relation to men congratulating men, or women congratulating women, or all of them together if all of them are Mahaarim (non-marriageable relatives), otherwise it is not permissible if the religious requirements are not met as discussed in Fatwa 82299.
Allaah Knows best.