Information from Wikipedia:

"Podmoskovnye Vechera" (Russian: "„P„€„t„}„€„ƒ„{„€„r„~„쳌„u „B„u„‰„u„‚„p", English: "Moscow Nights" or, more correctly, "Evenings of Moscow's Suburbs") - Russian lyrics by Mikhail Matusovsky, music by Vasily Solovyov-Sedoy, 1955. The British jazz group, Kenny Ball and his Jazzmen, had a hit with the song in 1961 under the title "Midnight in Moscow."

Russian lyrics and an English translation from http://www.pitt.edu/~slavic/sli/admin/moscow.html:

„P„€„t„}„€„ƒ„{„€„r„~„쳌„u „r„u„‰„u„‚„p

„N„u „ƒ„|„쳌„Š„~„쳌 „r „ƒ„p„t„… „t„p„w„u „Š„€„‚„€„‡„y,
„B„ƒ„v „x„t„u„ƒ„Ž „x„p„}„u„‚„|„€ „t„€ „…„„„‚„p.
E„ƒ„|„y „q „x„~„p„|„y „r„쳌, „{„p„{ „}„~„u „t„€„‚„€„s„y
„P„€„t„}„€„ƒ„{„€„r„~„쳌„u „r„u„‰„u„‚„p.

„Q„u„‰„{„p „t„r„y„w„u„„„ƒ„' „y „~„u „t„r„y„w„u„„„ƒ„',
„B„ƒ„' „y„x „|„…„~„~„€„s„€ „ƒ„u„‚„u„q„‚„p.
„P„u„ƒ„~„' „ƒ„|„쳌„Š„y„„„ƒ„' „y „~„u „ƒ„|„쳌„Š„y„„„ƒ„'
„B „쳌„„„y „„„y„‡„y„u „r„u„‰„u„‚„p.

„X„„„€ „w „q„쳌, „}„y„|„p„', „ƒ„}„€„„„‚„y„Š„Ž „y„ƒ„{„€„ƒ„p,
„N„y„x„{„€ „s„€„|„€„r„… „~„p„{„|„€„~„'?
„S„‚„…„t„~„€ „r„쳌„ƒ„{„p„x„p„„„Ž „y „~„u „r„쳌„ƒ„{„p„x„p„„„Ž
„B„ƒ„v, „‰„„„€ „~„p „ƒ„u„‚„t„ˆ„u „… „}„u„~„'.

„@ „‚„p„ƒ„ƒ„r„u„„ „…„w„u „r„ƒ„v „x„p„}„u„„„~„u„u.
„S„p„{, „쳌„€„w„p„|„…„z„ƒ„„„p, „q„…„t„Ž „t„€„q„‚„p.
„N„u „x„p„q„…„t„Ž „y „„„쳌 „쳌„„„y „|„u„„„~„y„u
„P„€„t„}„€„ƒ„{„€„r„~„쳌„u „r„u„‰„u„‚„p.

MOSCOW [AREA] NIGHTS
(translator's name not given)

Even whispers aren't heard in the garden,
Everything has died down till morning.
If you only knew how dear to me
Are these Moscow nights.

The river moves, unmoving,
All in silver moonlight.
A song is heard, yet unheard,
In these silent nights.

Why do you, dear, look askance,
With your head lowered so?
It is hard to express, and hard to hold back,
Everything that my heart holds.

But the dawn's becoming ever brighter.
So please, just be good.
Don't you, too, forget
These summer, Moscow nights.

Another English translation from http://brazilconcertband.org/next/russian.html (no title or translator's name given):
   
Not even a whisper is to be heard in the garden,
Everything has calmed down until dawn.
If you only knew how dear they are to me,
The evenings near Moscow!

The river is moving and (sometimes) not,
All made of the moons silver.
A song sounds and is not to be heard
In those quiet evenings.

Why do you, darling, look at me from the side,
Bending your head so low?
It is not easy to tell
All the things that are in my heart.

And dawn is getting more and more visible.
So, please, be so kind:
You, also, don쳌Lt forget
These summer evenings near Moscow.

[I don't know whether either of these English versions has been recorded.]