diff --git a/doc/doc-txt/OptionLists.txt b/doc/doc-txt/OptionLists.txt
index e7b2847605..3c64961618 100644
--- a/doc/doc-txt/OptionLists.txt
+++ b/doc/doc-txt/OptionLists.txt
@@ -617,6 +617,7 @@ tls_certificate                      string*         unset         main
 tls_dh_max_bits                      integer         2236          main              4.80
 tls_dh_min_bits                      integer         1024          smtp              4.82
 tls_dhparam                          string*         unset         main              3.20
+tls_ignore_missing_close_notify      boolean         true          main              (todo git master)
 tls_ocsp_file                        string*         unset         main              4.80 if experimental_ocsp
 tls_on_connect_ports                 string          unset         main              4.43
 tls_privatekey                       string*         unset         main              3.20
diff --git a/src/src/globals.c b/src/src/globals.c
index e887c27410..4a4b729b49 100644
--- a/src/src/globals.c
+++ b/src/src/globals.c
@@ -134,6 +134,7 @@ bit-count as "NORMAL" (2432) and Thunderbird dropping connection. */
 int     tls_dh_max_bits        = 2236;
 uschar *tls_dhparam            = NULL;
 uschar *tls_eccurve            = US"auto";
+BOOL    tls_ignore_missing_close_notify = TRUE;
 # ifndef DISABLE_OCSP
 uschar *tls_ocsp_file          = NULL;
 # endif
diff --git a/src/src/globals.h b/src/src/globals.h
index 5d912254d7..4b767423c3 100644
--- a/src/src/globals.h
+++ b/src/src/globals.h
@@ -138,6 +138,7 @@ extern uschar *tls_crl;                /* CRL File */
 extern int     tls_dh_max_bits;        /* don't accept higher lib suggestions */
 extern uschar *tls_dhparam;            /* DH param file */
 extern uschar *tls_eccurve;            /* EC curve */
+extern BOOL    tls_ignore_missing_close_notify; /* For semi-broken TLS servers like Gmail and Yandex */
 # ifndef DISABLE_OCSP
 extern uschar *tls_ocsp_file;          /* OCSP stapling proof file */
 # endif
diff --git a/src/src/readconf.c b/src/src/readconf.c
index 5ef776fea0..f016531d59 100644
--- a/src/src/readconf.c
+++ b/src/src/readconf.c
@@ -383,6 +383,7 @@ static optionlist optionlist_config[] = {
   { "tls_dh_max_bits",          opt_int,         {&tls_dh_max_bits} },
   { "tls_dhparam",              opt_stringptr,   {&tls_dhparam} },
   { "tls_eccurve",              opt_stringptr,   {&tls_eccurve} },
+  { "tls_ignore_missing_close_notify", opt_bool, {&tls_ignore_missing_close_notify} },
 # ifndef DISABLE_OCSP
   { "tls_ocsp_file",            opt_stringptr,   {&tls_ocsp_file} },
 # endif
diff --git a/src/src/tls-gnu.c b/src/src/tls-gnu.c
index 7963e2c97b..96da8ba7b7 100644
--- a/src/src/tls-gnu.c
+++ b/src/src/tls-gnu.c
@@ -4034,14 +4034,20 @@ do
 while (inbytes == GNUTLS_E_AGAIN);
 
 if (inbytes > 0) return inbytes;
-if (inbytes == 0)
+if (inbytes == 0
+    // there is a "bug" in Gmail and Yandex servers where they do not send the tls-protocol-mandated `close_notify` on connection close.
+    // They do it intentionally to save time (skip a roundtrip), but it is against tls-protocol and does spam the exim4 errorlogs like
+    // 2024-10-12 09:22:27 1szVWE-0071qn-2C H=gmail-smtp-in.l.google.com [142.250.102.27] TLS error on connection (recv_tls_read): The TLS connection was non-properly terminated.
+    // optionally treat this as a normal EOF.
+    // This is equivalent to OpenSSL's SSL_OP_IGNORE_UNEXPECTED_EOF flag.
+    || (tls_ignore_missing_close_notify && inbytes == GNUTLS_E_PREMATURE_TERMINATION))
   {
-  DEBUG(D_tls) debug_printf("Got TLS_EOF\n");
+    DEBUG(D_tls) debug_printf("Got TLS_EOF\n");
   }
 else
   {
-  DEBUG(D_tls) debug_printf("%s: err from gnutls_record_recv\n", __FUNCTION__);
-  record_io_error(state, (int)inbytes, US"recv", NULL);
+    DEBUG(D_tls) debug_printf("%s: err from gnutls_record_recv\n", __FUNCTION__);
+    record_io_error(state, (int)inbytes, US"recv", NULL);
   }
 
 return -1;
diff --git a/src/src/tls-openssl.c b/src/src/tls-openssl.c
index 302404b6c9..ef90c0a918 100644
--- a/src/src/tls-openssl.c
+++ b/src/src/tls-openssl.c
@@ -2954,6 +2954,12 @@ if (init_options)
 #ifdef OPENSSL_MIN_PROTO_VERSION
   SSL_CTX_set_min_proto_version(ctx, SSL3_VERSION);
 #endif
+#ifdef SSL_OP_IGNORE_UNEXPECTED_EOF
+  if(tls_ignore_missing_close_notify) {
+    init_options |= SSL_OP_IGNORE_UNEXPECTED_EOF;
+  }
+#endif
+
   DEBUG(D_tls) debug_printf("setting  SSL CTX options: %016lx\n", init_options);
   SSL_CTX_set_options(ctx, init_options);
    {