diff --git a/CHANGELOG.next.asciidoc b/CHANGELOG.next.asciidoc
index 5346ed8e976..3a5be54b8c7 100644
--- a/CHANGELOG.next.asciidoc
+++ b/CHANGELOG.next.asciidoc
@@ -151,6 +151,7 @@ https://github.com/elastic/beats/compare/v7.0.0-alpha2...master[Check the HEAD d
 - Fix bug with potential concurrent reads and writes from event.Meta map by Kafka output. {issue}14542[14542] {pull}14568[14568]
 - Fix spooling to disk blocking infinitely if the lock file can not be acquired. {pull}15338[15338]
 - Fix `metricbeat test output` with an ipv6 ES host in the output.hosts. {pull}15368[15368]
+- Fix `convert` processor conversion of string to integer with leading zeros. {issue}15513[15513] {pull}15557[15557]
 
 *Auditbeat*
 
diff --git a/libbeat/processors/convert/convert.go b/libbeat/processors/convert/convert.go
index fbc6b5b3014..887fbdd02a9 100644
--- a/libbeat/processors/convert/convert.go
+++ b/libbeat/processors/convert/convert.go
@@ -205,7 +205,7 @@ func toString(value interface{}) (string, error) {
 func toLong(value interface{}) (int64, error) {
 	switch v := value.(type) {
 	case string:
-		return strconv.ParseInt(v, 0, 64)
+		return strToInt(v, 64)
 	case int:
 		return int64(v), nil
 	case int8:
@@ -238,7 +238,7 @@ func toLong(value interface{}) (int64, error) {
 func toInteger(value interface{}) (int32, error) {
 	switch v := value.(type) {
 	case string:
-		i, err := strconv.ParseInt(v, 0, 32)
+		i, err := strToInt(v, 32)
 		return int32(i), err
 	case int:
 		return int32(v), nil
@@ -403,3 +403,24 @@ func cloneValue(value interface{}) interface{} {
 		return value
 	}
 }
+
+// strToInt is a helper to interpret a string as either base 10 or base 16.
+func strToInt(s string, bitSize int) (int64, error) {
+	base := 10
+	if hasHexPrefix(s) {
+		// strconv.ParseInt will accept the '0x' or '0X` prefix only when base is 0.
+		base = 0
+	}
+	return strconv.ParseInt(s, base, bitSize)
+}
+
+func hasHexPrefix(s string) bool {
+	if len(s) < 3 {
+		return false
+	}
+	a, b := s[0], s[1]
+	if a == '+' || a == '-' {
+		a, b = b, s[2]
+	}
+	return a == '0' && (b == 'x' || b == 'X')
+}
diff --git a/libbeat/processors/convert/convert_test.go b/libbeat/processors/convert/convert_test.go
index 2469fe1848c..141fafc0f8f 100644
--- a/libbeat/processors/convert/convert_test.go
+++ b/libbeat/processors/convert/convert_test.go
@@ -276,8 +276,16 @@ var testCases = []testCase{
 
 	{Long, nil, nil, true},
 	{Long, "x", nil, true},
+	{Long, "0x", nil, true},
+	{Long, "0b1", nil, true},
+	{Long, "1x2", nil, true},
 	{Long, true, nil, true},
 	{Long, "1", int64(1), false},
+	{Long, "-1", int64(-1), false},
+	{Long, "017", int64(17), false},
+	{Long, "08", int64(8), false},
+	{Long, "0X0A", int64(10), false},
+	{Long, "-0x12", int64(-18), false},
 	{Long, int(1), int64(1), false},
 	{Long, int8(1), int64(1), false},
 	{Long, int16(1), int64(1), false},
@@ -294,6 +302,17 @@ var testCases = []testCase{
 	{Integer, nil, nil, true},
 	{Integer, "x", nil, true},
 	{Integer, true, nil, true},
+	{Integer, "x", nil, true},
+	{Integer, "0x", nil, true},
+	{Integer, "0b1", nil, true},
+	{Integer, "1x2", nil, true},
+	{Integer, true, nil, true},
+	{Integer, "1", int32(1), false},
+	{Integer, "-1", int32(-1), false},
+	{Integer, "017", int32(17), false},
+	{Integer, "08", int32(8), false},
+	{Integer, "0X0A", int32(10), false},
+	{Integer, "-0x12", int32(-18), false},
 	{Integer, "1", int32(1), false},
 	{Integer, int(1), int32(1), false},
 	{Integer, int8(1), int32(1), false},