Taken directly from shia blog, just with slight edition:

Majlisi said in “Biharul anwar” (30/399):

أقول: الأخبار الدالة على كفر أبي بكر وعمر وأضرابهما وثواب لعنهم والبراءة منهم وما يتضمن بدعهم أكثر من أن يذكر في هذا المجلد أو في مجلدات شتى وفيما أوردنا كفاية لمن أراد الله هدايته إلى الصراط 

I  say: The ahadith evidence upon the kufr of Abu Bakr and Umar and their chastising, as well as the thawab (reward) for doing la’nah (damnation) upon them and dissociating from them and what is included in their bid’ahs (innovations), most of which has been mentioned in this volume or in other volumes. And what has been stated is sufficient for one to whom Allah (swt) wills to guide him to the straight path.

Majlisi also said in “Jilal al-Uyon” (p 45):

 لا مجال لعاقل أن يشك في كفر عمر فلعنة الله ورسوله عليه وعلى من اعتبره مسلماً وعلى من يكف عن لعنه

“It is impossible for a sane person to doubt the kufr of Umar, so la’nah (damnation) of Allah (swt) and His messenger (pbuh) upon him and upon anyone who considers him a Muslim and anyone who restrains from doing la’nah on him.”  

Muhaqqiq al Karki wrote in his book Nufhat al Ahwat (page 198),  after quoting some ahadith regarding kufr and damnation (la’nah) of the caliphs:

 وهذا النحو في كتب أصحابنا مما لو تحرّى المتصدي لحصره جمع منه مجلدات ولم يأت على آخره، وقد أورد الأمين الضابط الثقة محمد بن يعقوب الكليني في كتابه ” الكافي “من ذلك شيئاً كثيراً، وفيه أحاديث باللعن الصريح، والحث عليه من الأئمة

“And it is similar in the books of our companions (i.e. ahadith about lan’ah and takfeer upon shaikhain), if someone stood to compile them into volumes it would be never ending, and Shaikh Kulaini has stated a lot of such ahadith in his book al Kafi and the Imams (as) had encouraged it.”

Kulayni in his “al-Kafi” (volume 8, p 245, 246) narrated:

340- Ali b. Ibrahim, from his father, from Hannan b. Sudir and Muhammad b. Yahya, from Ahmad b. Muhammad b. Ismail, from Hannan b. Sudir from his father who said: I asked aba Ja’far (as) about them both, so he (as) said: “O aba al Fadhal! Do not ask me about those two because by Allah none of us ever dies without being discontented with them, and till this day there is none among us but that he is discontented with them. The elder among us bequeaths this (i.e. about discontentment with those two) to the young ones. Verily they suppressed our right and prohibited us from it, and they were the first to mount our necks and transgress upon us, transgression in Islam will now never stop until our Qaim (Imam Mahdi) rises or our speaker speaks.

He (as) then said: But by Allah! If our Qaim rose and our speaker spoke, their affairs which were hidden would be revealed and their issues/innovations which our apparent would be hidden (erased). By Allah! No affliction or trouble afflicts us ahlulbayt (as) but that those two are its root cause, so upon them be la’nah (damnation) of Allah, the angels and all the people.

343- Hannan from his father, from abi Ja’far (as), he (narrator) said: I said to him (as): “Were the children of Ya’qoob (as) prophets?” Imam (as) said: “No, but they were grandchildren of offspring of the prophets, and they did not depart from the world except happily (for) they repented and remembered what they had done whereas the shaikhain departed the world and did not repent and did not remember/reflect on what they did to commander of the faithful [Ali (as)], so on them is la’nah (damnation) of Allah (swt) and the angels and all the people.”

In Miratul uqool by Allama Majlisi (1111 AH)  (26/212) first hadith graded as Hasan or Muwathaq, and second also Hasan or Muwathaq (Good or reliable).

Majlisi in “Biharul anwar” (69/137) said:

25 تقريب المعارف لابي الصلاح الحلبي : عن أبي علي الخراساني عن مولى لعلي بن الحسن عليه السلام قال : كنت معه عليه السلام في بعض خلواته فقلت : إن لي عليك حقا ألا تخبرني عن هذين الرجلين : عن أبي بكر وعمر ؟ فقال : كافران كافر من أحبهما
وعن أبي حمزة الثمالي أنه سئل علي بن الحسين عليهما السلام عنهما فقال : كافران كافر من تولاهما

25- Taqrib al Mu’arif by abi Salah al Halabi: From abi Ali al Khurasani, from a servant of Ali b. al Hussain (as) who said: I was with him (as) in some of his retreats, so I said: Indeed I have a right upon you, do a favor of informing me about the state of the two men: about Abu Bakr and Umar? So he (as) said: “Both are kafirs (disbelievers), one who likes them is (also) a kafir.”

And from abi Hamza al Thamali that he asked Ali b. al Hussain (as) about them, so he (as) said: “They both are kafirs and one who loves them is also a kafir.”