A doctor was interrupted in the middle of his own chuppah because someone in the audience had an emergency that required the doctor's help. The emergency occured at the point where the groom was holding the ring and about to place it on the bride's finger, but the witnesses weren't yet called up. Just prior to leaving the chuppah, he quickly placed the ring on the bride's finger, but did not recite the "harei at ..." declaration. Is he halachically married or does he have to repeat the chuppah?
I am not a rabbi. That being said:
If he's at the chuppah, then the "harei at..." is probably not necessary, since both the groom and the bride obviously agree to the marriage.
However, the witnesses are absolutely required. If they did not see the groom put the ring on the bride's finger, then the marriage is not valid. If there are others (unrelated to both parties) watching, but they were not designated as witnesses, it may be valid.
In all cases, the ceremony should probably be repeated with a new ring (or other item of value). Furthermore, the remaining part of the wedding is also required, viz. the Sheva Berachos and the yichud room.
Editing my answer in light of potential misunderstanding of Rambam:
From Rambam ishut 3:2 it seems that a formulation of words indicating he is buying her had in marriage needs to be said in order to marry her:
כיצד האשה מתקדשת. אם בכסף הוא מקדש אין פחות מפרוטה כסף או שוה פרוטה. אומר לה הרי את מקודשת לי. או הרי את מאורסת לי. או הרי את לי לאשה בזה. ונותן לה בפני עדים. והאיש הוא שאומר דברים שמשמען שקונה אותה לו לאשה והוא שיתן לה הכסף.
How is the bond of kiddushin established with a woman? If the man [desires to establish] the kiddushin by [the transfer of] money, [he must give] a p'rutah, either in coin or its worth. [Before giving it], he tells her, "You are consecrated unto me...," "You are betrothed to me...," or "You become my wife through this." He must give her [the money or the item] in the presence of witnesses. It is the man who makes the statement that implies that he acquires the woman as his wife, and it is he who gives her the money.
This is emphasized in halacha 6:
הדברים שיאמר האיש כשיקדש צריך שיהיה משמעם שהוא קונה האשה ולא שיהא משמע שהקנה עצמו לה. כיצד הרי שאמר לה או שכתב בשטר שנתנו לה. הריני בעליך. הריני ארוסיך. הריני אישיך וכל כיוצא בזה. אין כאן קידושין כלל The statements that the man makes when he consecrates [his wife] must imply that he acquires her as a wife, and not that he gives himself to her. What is implied? Should he tell her, or write in the document he gives her: "I am your husband," "I am your betrothed," "I am your man," or the like, the marriage bond is not established at all.
From these two sources, as long as he hasn't said Harei At Mekudeshet li, the fact that both parties agree is immaterial, he would still need to go and give her the ring along with the declaration.
In 3:8, the Rambam however says:
היה מדבר עם האשה על עסקי הקידושין ורצתה ועמד וקידש ולא פירש ולא אמר לה כלום אלא נתן בידה או בעל הואיל והן עסוקין בענין דיו ואינו צריך לפרש.
If a man was speaking to a woman about consecrating her and she consented, and he immediately gave her [something] in her hand to consecrate her or engaged in sexual relations [with that intent], without [making a statement] clarifying [his purpose], it is sufficient. Since they were speaking about this matter, it is not necessary for him to be explicit.
From this halacha, as @DoubleAA pointed out it seems that as long as the context is one of marriage, we do not require an explicit declaration. This Rambam, however, might also be understood to mean that the speaking about the context in such a way that she acquiesces to his proposal replaces the formulation. This would explain why the Rambam groups the halacha with the idea of what constitutes a proposal:
ויש לאיש לקדש האשה בכל לשון שהיא מכרת בו. ויהיה משמע הדברים באותה הלשון שקנאה כמו שביארנו. A man may consecrate a woman by making statements in any language that she understands, provided that, in that language, his statements mean that he is acquiring her, as explained.
I have no proof that the Rambam requires their to be an actual acquiescence at the time of receiving the ring, but struggle to understand the 2nd and 6th halachot any other way. As such, it seems to me that even in the context of the wedding, until the bride actually acquiesces verbally, as the Rambam writes ורצתה, the marriage is incomplete. Unfortunately, this answer is mostly pilpul, and should most certainly not be relied on for any practical purposes (even more so than usual).
The witnesses are also vital to the process and without them the marriage is problematic. See Rambam Ishut 1:1.